An Eigenvalue Problem with variable exponents

Giovanni Franzina; Peter Lindqvist

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arXiv · 1210.1397

An Eigenvalue Problem with variable exponents

Giovanni Franzina·Peter Lindqvist

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Abstract

A highly nonlinear eigenvalue problem is studied in a Sobolev space with variable exponent. The Euler-Lagrange equation for the minimization of a Rayleigh quotient of two Luxemburg norms is derived. The asymptotic case with a "variable infinity" is treated. Local uniqueness is proved for the viscosity solutions.

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Giovanni Franzina, Peter Lindqvist. 2012-10-04. An Eigenvalue Problem with variable exponents. https://arxiv.org/abs/1210.1397

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