An Eigenvalue Problem with variable exponents

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.

References in corpus (1)

• The \infty eigenvalue problem and a problem of optimal transportation