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MiS Preprint
8/2003

Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition

Miroslav Chlebík, Marek Fila and Wolfgang Reichel

Abstract

We study the existence of positive solutions of a linear elliptic equation with critical Sobolev exponent in a nonlinear Neumann boundary condition. We prove a result which is similar to a classical result of Brezis and Nirenberg who considered a corresponding problem with nonlinearity in the equation. Our proof of the fact that the dimension three is critical use a new Pohozaev-type identity.

Received:
Feb 7, 2003
Published:
Feb 7, 2003
MSC Codes:
35J65, 35B33
Keywords:
critical sobolev exponent, nonlinear boundary condition

Related publications

inJournal
2003 Repository Open Access
Miroslav Chlebik, Marek Fila and Wolfgang Reichel

Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition

In: Nonlinear differential equations and applications, 10 (2003) 3, pp. 329-346