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Generalized Pohožaev and Pucci-Serrin identities and non-existence results for p(x)-Laplacian type equations

Content Provider	Springer Nature Link
Author	Dinca, George Isaia, Florin
Copyright Year	2010
Abstract	In this article, generalizations of the well-known Pohožaev and Pucci-Serrin identities and (as consequences of them) some non-existence results for Dirichlet problems with p (x)-Laplacian are obtained.The main ideas within this paper as well as the most important results obtained during the study are presented in Section 1.In Section 2, there are recalled the main results concerning the generalized Sobolev spaces (also known as Sobolev spaces with variable exponent)which will be used throughout this paper.In Sections 3 and 4, we will give some necessary technical results regarding the differential calculus in generalized Sobolev spaces and the differentiability properties of superposition operators between generalized Sobolev spaces (in the Marcus-Mizel direction).In Sections 5 and 6, a Pohožaev-type identity and a non-existence result obtained by Pucci and Serrin for a Dirichlet problem with p-Laplacian are generalized to a Dirichlet problem with p (x)-Laplacian. The Pohožaev identity and the non-existence Pohožaev’s result for Dirichlet problems with Laplacian are also generalized to the case of p (x)-Laplacian. In order to achieve this generalization, the technical results from Sections 3 and 4 are involved.
Starting Page	1
Ending Page	46
Page Count	46
File Format	PDF
ISSN	0009725X
Journal	Rendiconti del Circolo Matematico di Palermo
Volume Number	59
Issue Number	1
e-ISSN	19734409
Language	English
Publisher	Springer Milan
Publisher Date	2010-04-27
Publisher Place	Milan
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Chain rule p (x)-Laplacian Generalized Pohožaev identity Generalized Pucci-Serrin identity Non-existence theorem Boundary value problems for nonlinear higher-order equations Degenerate elliptic equations Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems Particular nonlinear operators Applications of Mathematics Analysis Geometry Algebra Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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