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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.
