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Positive solutions of linear elliptic equations with critical growth in the Neumann boundary condition
journal contribution
posted on 2023-06-08, 06:43 authored by Miroslav ChlebikMiroslav Chlebik, Marek Fila, Wolfgang ReichelWe 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 uses a new Pohozaev-type identity.
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Publication status
- Published
Journal
Nonlinear Differential Equations and ApplicationsISSN
1021-9722Publisher
Springer VerlagExternal DOI
Issue
3Volume
10Page range
329-346Department affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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