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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition
Miroslav Chlebík, Marek Fila and Wolfgang ReichelAbstract
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:
- 07.02.03
- Published:
- 07.02.03
- MSC Codes:
- 35J65, 35B33
- Keywords:
- critical sobolev exponent, nonlinear boundary condition