The pseudo-$p$-Laplace eigenvalue problem and viscosity solutions as $p\to \infty$

Belloni, Marino; Kawohl, Bernd

ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 28-52.

We consider the pseudo-$p$-laplacian, an anisotropic version of the $p$-laplacian operator for $p\ne 2$. We study relevant properties of its first eigenfunction for finite $p$ and the limit problem as $p\to \infty$.

Classification : 35P30, 35B30, 49R50, 35P15
Mots clés : eigenvalue, anisotropic, pseudo-Laplace, viscosity solution, minimal Lipschitz extension, concavity, symmetry, convex rearrangement

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