Advances in Differential Equations

Generalized Pohozaev identity and a non-existence result for the p-Laplacian: weak solutions

George Dinca and Florin Isaia

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Abstract

In this paper, a generalization of the well-known Pohožaev identity and a non-existence result for some Dirichlet problems with the p-Laplacian are obtained. As a preliminary, we will give some necessary technical results regarding the differential calculus in Sobolev spaces and the differentiability properties of superposition operators between Sobolev spaces (in the Marcus-Mizel direction).

Article information

Source
Adv. Differential Equations Volume 14, Number 5/6 (2009), 497-540.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867258

Mathematical Reviews number (MathSciNet)
MR2502703

Zentralblatt MATH identifier
1179.35132

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) [See also 45Gxx, 45P05] 35G30: Boundary value problems for nonlinear higher-order equations 35J70: Degenerate elliptic equations

Citation

Dinca, George; Isaia, Florin. Generalized Pohozaev identity and a non-existence result for the p-Laplacian: weak solutions. Adv. Differential Equations 14 (2009), no. 5/6, 497--540. https://projecteuclid.org/euclid.ade/1355867258.


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