CodiceQDD 31
TitoloNodal solutions to critical growth elliptic problems under Steklov boundary conditions
Data2008-07-08
Autore/iBerchio,E.; Gazzola,F.; Pierotti,D.
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PubblicatoCommunications on Pure and Applied Analysis
AbstractWe study elliptic problems at critical growth under Steklov boundary conditions in bounded domains. For a second order problem we prove existence results for nontrivial nodal solutions. These are obtained by combining a suitable linking argument with ¯ne estimates on the concentration of Sobolev minimizers on the boundary. When the domain is the unit ball, we improve these results by taking advantage of the explicit form of the Steklov eigenfunctions. We also partially extend the results in the ball to the case of fourth order Steklov boundary value problems.