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Science/Engineering A First Course in Sobolev Spaces

Posted on 2010-08-07




Name:Science/Engineering A First Course in Sobolev Spaces
ASIN/ISBN:0821847686
Author:Giovanni Leoni
Publisher:American Mathematical Society
Publish Date:2009
Language:English
Pages:626
File size:2.3 Mb
   Science/Engineering A First Course in Sobolev Spaces

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There are two ways to introduce Sobolev spaces: The first is through the elegant (and abstract) theory of distributions developed by Laurent Schwartz in the late 1940s; the second is to look at them as the natural development and unfolding of monotone, absolutely continuous, and BV functions' of one variable. To my knowledge, this is one of the first books to follow the second approach. I was more or less forced into it: This book is based on a series of lecture notes that I wrote for the graduate course "Sobolev Spaces", which I taught in the fall of 2006 and then again in the fall of 2008 at Carnegie Mellon University. In 2006, during the first lecture, I found out that half of the students were beginning graduate students with no background in functional analysis (which was offered only in the spring) and very little in measure theory (which, luckily, was offered in the fall). At that point I had two choices: continue with a classical course on Sobolev spaces and thus loose half the class after the second lecture or toss my notes and rethink the entire operation, which is what I ended up doing.

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