The pseudo-$p$-Laplace eigenvalue problem and viscosity solutions as ${p\rightarrow \infty }$

Belloni, Marino; Kawohl, Bernd

doi:10.1051/cocv:2003035

Geodesic

Parcourir par

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

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Résumé

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

MR Zbl

DOI : 10.1051/cocv:2003035

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

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     author = {Belloni, Marino and Kawohl, Bernd},
     title = {The pseudo-$p${-Laplace} eigenvalue problem and viscosity solutions as ${p\rightarrow \infty }$},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {28--52},
     publisher = {EDP-Sciences},
     volume = {10},
     number = {1},
     year = {2004},
     doi = {10.1051/cocv:2003035},
     mrnumber = {2084254},
     zbl = {1092.35074},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003035/}
}

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Belloni, Marino; Kawohl, Bernd. The pseudo-$p$-Laplace eigenvalue problem and viscosity solutions as ${p\rightarrow \infty }$. ESAIM: Control, Optimisation and Calculus of Variations, Tome 10 (2004) no. 1, pp. 28-52. doi: 10.1051/cocv:2003035

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