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Sobolev Spaces

2018
AbstractThis chapter presents a selection of some of the most important results in the theory of Sobolev spacesn. Special emphasis is placed on embedding theorems and the question as to whether an embedding map is compact or not. Some results concerning the k-set contraction nature of certain embedding maps are given, for both bounded and unbounded ...
D. E. Edmunds, W. D. Evans
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Hardy's Inequality in a Variable Exponent Sobolev Space

Georgian Mathematical Journal, 2005
We show that a norm version of Hardy's inequality holds in a variable exponent Sobolev space provided the maximal operator is bounded. Our proof uses recent local versions of the inequality for a fixed exponent.
Petteri Harjulehto, P. Hst, M. Koskenoja
semanticscholar   +1 more source

Sobolev Spaces

2021
George C. Hsiao, Wolfgang L. Wendland
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Sobolev spaces

2007
Abstract In this chapter we define Sobolev spaces which are the ‘natural’ spaces of functions in which to solve variational formulations of partial differential equations. Physically, Sobolev spaces can be interpreted as spaces of functions with finite energy.
openaire   +2 more sources

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