Textbook recommendation request: Exercises to supplement Evans and Gariepy












8












$begingroup$


While a great book about measure theory and real analysis in $mathbb R^n$, the only downside is the lack of exercises. Can anyone provide a good book to supplement it with exercises? I plan to use it for self study.






real-analysis geometric-measure-theory textbook-recommendation







share|cite|improve this question









$endgroup$












  • $begingroup$
    Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
    $endgroup$
    – Y.B.
    Jan 15 at 12:52










  • $begingroup$
    Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
    $endgroup$
    – Y.B.
    Jan 15 at 12:54










  • $begingroup$
    I will check out the first one, seems interesting!
    $endgroup$
    – James Baxter
    Jan 15 at 12:55






  • 1




    $begingroup$
    This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
    $endgroup$
    – Piotr Hajlasz
    Jan 15 at 13:05
















8












$begingroup$


While a great book about measure theory and real analysis in $mathbb R^n$, the only downside is the lack of exercises. Can anyone provide a good book to supplement it with exercises? I plan to use it for self study.






real-analysis geometric-measure-theory textbook-recommendation







share|cite|improve this question









$endgroup$












  • $begingroup$
    Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
    $endgroup$
    – Y.B.
    Jan 15 at 12:52










  • $begingroup$
    Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
    $endgroup$
    – Y.B.
    Jan 15 at 12:54










  • $begingroup$
    I will check out the first one, seems interesting!
    $endgroup$
    – James Baxter
    Jan 15 at 12:55






  • 1




    $begingroup$
    This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
    $endgroup$
    – Piotr Hajlasz
    Jan 15 at 13:05














8












8








8


4



$begingroup$


While a great book about measure theory and real analysis in $mathbb R^n$, the only downside is the lack of exercises. Can anyone provide a good book to supplement it with exercises? I plan to use it for self study.






real-analysis geometric-measure-theory textbook-recommendation







share|cite|improve this question









$endgroup$




While a great book about measure theory and real analysis in $mathbb R^n$, the only downside is the lack of exercises. Can anyone provide a good book to supplement it with exercises? I plan to use it for self study.






real-analysis geometric-measure-theory textbook-recommendation




real-analysis geometric-measure-theory textbook-recommendation






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jan 15 at 12:44









James BaxterJames Baxter

32313




32313












  • $begingroup$
    Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
    $endgroup$
    – Y.B.
    Jan 15 at 12:52










  • $begingroup$
    Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
    $endgroup$
    – Y.B.
    Jan 15 at 12:54










  • $begingroup$
    I will check out the first one, seems interesting!
    $endgroup$
    – James Baxter
    Jan 15 at 12:55






  • 1




    $begingroup$
    This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
    $endgroup$
    – Piotr Hajlasz
    Jan 15 at 13:05


















  • $begingroup$
    Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
    $endgroup$
    – Y.B.
    Jan 15 at 12:52










  • $begingroup$
    Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
    $endgroup$
    – Y.B.
    Jan 15 at 12:54










  • $begingroup$
    I will check out the first one, seems interesting!
    $endgroup$
    – James Baxter
    Jan 15 at 12:55






  • 1




    $begingroup$
    This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
    $endgroup$
    – Piotr Hajlasz
    Jan 15 at 13:05
















$begingroup$
Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
$endgroup$
– Y.B.
Jan 15 at 12:52




$begingroup$
Have you given a look to Functions of Bounded Variation and Free Discontinuity Problems (Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs? The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.
$endgroup$
– Y.B.
Jan 15 at 12:52












$begingroup$
Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
$endgroup$
– Y.B.
Jan 15 at 12:54




$begingroup$
Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer.
$endgroup$
– Y.B.
Jan 15 at 12:54












$begingroup$
I will check out the first one, seems interesting!
$endgroup$
– James Baxter
Jan 15 at 12:55




$begingroup$
I will check out the first one, seems interesting!
$endgroup$
– James Baxter
Jan 15 at 12:55




1




1




$begingroup$
This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
$endgroup$
– Piotr Hajlasz
Jan 15 at 13:05




$begingroup$
This is a very good question since it is really difficult to find a reasonable collection of problems in elementary geometric measure theory and Sobolev spaces.
$endgroup$
– Piotr Hajlasz
Jan 15 at 13:05










2 Answers
2






active

oldest

votes


















5












$begingroup$

If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:



A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).



This is a great collection of problems with complete solutions.



However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book



W. P. Ziemer, Weakly Differentiable Functions. Sobolev spaces and functions of bounded variation..
Graduate Texts in Mathematics, 120. Springer-Verlag, New York, 1989.
(MathSciNet review).



presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.






share|cite|improve this answer











$endgroup$









  • 2




    $begingroup$
    What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
    $endgroup$
    – Y.B.
    Jan 15 at 13:14



















3












$begingroup$

Concerning Geometric measure theory and BV functions, I would recommend Functions of Bounded Variation and Free Discontinuity Problems (by Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs. The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.



Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer, at least for exercises concerning the one-dimensional case.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
    $endgroup$
    – Piotr Hajlasz
    Jan 15 at 13:02










  • $begingroup$
    @PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
    $endgroup$
    – Y.B.
    Jan 15 at 13:06











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2 Answers
2






active

oldest

votes








2 Answers
2






active

oldest

votes









active

oldest

votes






active

oldest

votes









5












$begingroup$

If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:



A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).



This is a great collection of problems with complete solutions.



However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book



W. P. Ziemer, Weakly Differentiable Functions. Sobolev spaces and functions of bounded variation..
Graduate Texts in Mathematics, 120. Springer-Verlag, New York, 1989.
(MathSciNet review).



presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.






share|cite|improve this answer











$endgroup$









  • 2




    $begingroup$
    What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
    $endgroup$
    – Y.B.
    Jan 15 at 13:14
















5












$begingroup$

If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:



A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).



This is a great collection of problems with complete solutions.



However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book



W. P. Ziemer, Weakly Differentiable Functions. Sobolev spaces and functions of bounded variation..
Graduate Texts in Mathematics, 120. Springer-Verlag, New York, 1989.
(MathSciNet review).



presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.






share|cite|improve this answer











$endgroup$









  • 2




    $begingroup$
    What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
    $endgroup$
    – Y.B.
    Jan 15 at 13:14














5












5








5





$begingroup$

If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:



A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).



This is a great collection of problems with complete solutions.



However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book



W. P. Ziemer, Weakly Differentiable Functions. Sobolev spaces and functions of bounded variation..
Graduate Texts in Mathematics, 120. Springer-Verlag, New York, 1989.
(MathSciNet review).



presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.






share|cite|improve this answer











$endgroup$



If you look for a generic collection of problems in measure theory and functional analysis, I would highly recommend:



A. Torchinsky, Problems in real and functional analysis. Graduate Studies in Mathematics, 166. American Mathematical Society, Providence, RI, 2015.
(MathSciNet review).



This is a great collection of problems with complete solutions.



However, if you are looking more for a collection of problems in geometric measure they and Sobolev spaces, as it is represented in the book by Evans and Gariepy, it is difficult to find one. However, the book



W. P. Ziemer, Weakly Differentiable Functions. Sobolev spaces and functions of bounded variation..
Graduate Texts in Mathematics, 120. Springer-Verlag, New York, 1989.
(MathSciNet review).



presents material similar to that in the book by Evans and Gariepy and it includes many exercises. Unfortunately the exercises do not have solutions.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Jan 23 at 1:54

























answered Jan 15 at 13:01









Piotr HajlaszPiotr Hajlasz

8,36942865




8,36942865








  • 2




    $begingroup$
    What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
    $endgroup$
    – Y.B.
    Jan 15 at 13:14














  • 2




    $begingroup$
    What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
    $endgroup$
    – Y.B.
    Jan 15 at 13:14








2




2




$begingroup$
What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
$endgroup$
– Y.B.
Jan 15 at 13:14




$begingroup$
What a nice book the one by Torchinksy, I did not know it! It is a pity it does not have exercises on GMT. It reminds me somehow of the Costara-Popa (which is btw more on the functional analytic point of view). Thanks in any case for pointing it out!
$endgroup$
– Y.B.
Jan 15 at 13:14











3












$begingroup$

Concerning Geometric measure theory and BV functions, I would recommend Functions of Bounded Variation and Free Discontinuity Problems (by Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs. The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.



Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer, at least for exercises concerning the one-dimensional case.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
    $endgroup$
    – Piotr Hajlasz
    Jan 15 at 13:02










  • $begingroup$
    @PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
    $endgroup$
    – Y.B.
    Jan 15 at 13:06
















3












$begingroup$

Concerning Geometric measure theory and BV functions, I would recommend Functions of Bounded Variation and Free Discontinuity Problems (by Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs. The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.



Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer, at least for exercises concerning the one-dimensional case.






share|cite|improve this answer











$endgroup$













  • $begingroup$
    Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
    $endgroup$
    – Piotr Hajlasz
    Jan 15 at 13:02










  • $begingroup$
    @PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
    $endgroup$
    – Y.B.
    Jan 15 at 13:06














3












3








3





$begingroup$

Concerning Geometric measure theory and BV functions, I would recommend Functions of Bounded Variation and Free Discontinuity Problems (by Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs. The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.



Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer, at least for exercises concerning the one-dimensional case.






share|cite|improve this answer











$endgroup$



Concerning Geometric measure theory and BV functions, I would recommend Functions of Bounded Variation and Free Discontinuity Problems (by Luigi Ambrosio, Nicola Fusco, and Diego Pallara), Oxford Mathematical Monographs. The first two-three chapters may be of interest to you and they contain (non-trivial) exercises.



Concerning Sobolev spaces, I would also recommend the well known book by Brezis, Functional Analysis, Springer, at least for exercises concerning the one-dimensional case.







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Jan 15 at 13:07

























answered Jan 15 at 13:00









Y.B.Y.B.

14312




14312












  • $begingroup$
    Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
    $endgroup$
    – Piotr Hajlasz
    Jan 15 at 13:02










  • $begingroup$
    @PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
    $endgroup$
    – Y.B.
    Jan 15 at 13:06


















  • $begingroup$
    Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
    $endgroup$
    – Piotr Hajlasz
    Jan 15 at 13:02










  • $begingroup$
    @PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
    $endgroup$
    – Y.B.
    Jan 15 at 13:06
















$begingroup$
Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
$endgroup$
– Piotr Hajlasz
Jan 15 at 13:02




$begingroup$
Brezis does not have exercises in Sobolev spaces except Sobolev spaces in dimension one.
$endgroup$
– Piotr Hajlasz
Jan 15 at 13:02












$begingroup$
@PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
$endgroup$
– Y.B.
Jan 15 at 13:06




$begingroup$
@PiotrHajlasz Uh you are right, I thought it had problems also for multi-d case, but I got confused, you are right. Thanks!
$endgroup$
– Y.B.
Jan 15 at 13:06


















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