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**A First Course in Sobolev Spaces**

Giovanni Leoni

Publication Year: 2009

ISBN-10: 0-8218-4768-6

ISBN-13: 978-0-8218-4768-8

Graduate Studies in Mathematics*,* vol. 105

*Contact information*:

- Giovanni Leoni
- Department of Mathematical Sciences
- Carnegie Mellon University
- 5000 Forbes Avenue
- Pittsburgh, PA 15213
- giovanni@andrew.cmu.edu
- http://www.math.cmu.edu/math/faculty/leoni.html

**Corrections and Improvements** as a PDF file. Posted 29-July-2016

Dedication page as a PDF file. Posted 24-September-2009. [10 KB]

An extension of the Sobolev--Gagliardo--Nirenberg theorem as a PDF file. Posted 05-August-2009. [109 KB]

Traces of functions in W^{k,p}(Half space) as a PDF file. Posted 24-September-2009. [115 KB]

Higher order Besov spaces as a PDF file. Posted 24-September-2009. [228 KB]

An alternative proof of Proposition 16.21 as a PDF file. Posted 30-June-2011. [81 KB]

Riesz potentials and embedding theorems as a PDF file. Posted 13-May-2010. [155 KB]

Interpolation for intermediate derivatives as a PDF file. Posted 29-July-2010. [144 KB]

A simpler proof of Theorem 10.29 as a PDF file. Posted 09-August-2012 [75 KB]

Yet another proof of Theorem 1.21 as a PDF file. Posted 11-October-2012 [78 KB]

An alternative proof of Theorem 3.30 as a PDF file. Posted 11-October-2012 [87 KB]

An alternative proof of Theorem 7.2 as a PDF file. Posted 11-October-2012 [73 KB]

A simpler proof of Theorem 11.51 as a PDF file. Posted 08-November-2012 [65 KB]

On Theorems 11.23 and 11.29 as a PDF file. Posted 01-February-2013. [89 KB]

On Theorem 10.35 as a PDF file. Posted 09-October-2014

Extension of higher order Sobolev functions as a PDF file. Posted 09-October-2014

A simpler proof of Theorem C.19 as a PDF file. Posted 09-October-2014

A simpler proof of Theorem 15.8 (iii) as a PDF file. Posted 14-November-2014

From *Math Reviews: *as PDF [62 KB], as active link