Differential and Integral Equations

The anisotropic $\infty$-Laplacian eigenvalue problem with Neumann boundary conditions

Gianpaolo Piscitelli

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We analyze the limiting problem for the anisotropic $p$-Laplacian ($p\rightarrow\infty$) on convex sets, with the mean of the viscosity solution. We also prove some geometric properties of eigenvalues and eigenfunctions. In particular, we show the validity of a Szegö-Weinberger type inequality.

Article information

Differential Integral Equations, Volume 32, Number 11/12 (2019), 705-734.

First available in Project Euclid: 22 October 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory 35P15: Estimation of eigenvalues, upper and lower bounds 35D40: Viscosity solutions 35J70: Degenerate elliptic equations


Piscitelli, Gianpaolo. The anisotropic $\infty$-Laplacian eigenvalue problem with Neumann boundary conditions. Differential Integral Equations 32 (2019), no. 11/12, 705--734. https://projecteuclid.org/euclid.die/1571731516

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