We study elliptic problems at critical growth under Steklov boundary conditions in bounded domains. For a second order problem we prove existence of nontrivial nodal solutions. These are obtained by combining a suitable linking argument with fine estimates on the concentration of Sobolev minimizers on the boundary. When the domain is the unit ball, we obtain a multiplicity result 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.

Nodal solutions to critical growth elliptic problems under Steklov boundary conditions / Berchio, Elvise; F., Gazzola; D., Pierotti. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 8 (2):(2009), pp. 533-557. [10.3934/cpaa.2009.8.533]

Nodal solutions to critical growth elliptic problems under Steklov boundary conditions

BERCHIO, ELVISE;
2009

Abstract

We study elliptic problems at critical growth under Steklov boundary conditions in bounded domains. For a second order problem we prove existence of nontrivial nodal solutions. These are obtained by combining a suitable linking argument with fine estimates on the concentration of Sobolev minimizers on the boundary. When the domain is the unit ball, we obtain a multiplicity result 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2522497
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