Calculus of Variations and Geometric Measure Theory
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D. Mugnai

Asymptotic behaviour, nodal lines and symmetry properties for solutions of superlinear elliptic equations near an eigenvalue

created by mugnai on 07 Nov 2007


Published Paper

Inserted: 7 nov 2007

Volume: 11
Number: 4
Pages: 508-521
Year: 2005


We give the precise behaviour of some solutions of a nonlinear elliptic B.V.P. in a bounded domain when a parameter approaches an eigenvalue of the principal part. If the nonlinearity has some regularity and the domain is for example convex, we also prove a nonlinear version of Courant's Nodal Theorem.

Keywords: eigenvalues, $L^\infty-H_0^1$ estimate, nodal lines, symmetries


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