Calculus of Variations and Geometric Measure Theory

G. Franzina - P. Lindqvist

An eigenvalue problem with variable exponents

created by franzina on 04 Oct 2012
modified on 05 Dec 2013


Published Paper

Inserted: 4 oct 2012
Last Updated: 5 dec 2013

Journal: Nonlinear Analysis
Volume: 85
Pages: 1-16
Year: 2013


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.