Eigenvalues for double phase variational integrals

2015/07/07 by Francesca Colasuonno, Marco Squassina, Colasuonno, Francesca +1 · 1 citation
Mathematics · #35J92 #35P30 #47A75 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J92 #msc:35P30 #msc:47A75

paper · pdf · doi:10.48550/arxiv.1507.01959

42 pages, typos corrected, final version, to appear in Ann. Mat. Pura Appl

arxiv created 2015/10/10 · arxiv updated 2015/10/13

Abstract

We study an eigenvalue problem in the framework of double phase variational integrals and we introduce a sequence of nonlinear eigenvalues by a minimax procedure. We establish a continuity result for the nonlinear eigenvalues with respect to the variations of the phases. Furthermore, we investigate the growth rate of this sequence and get a Weyl-type law consistent with the classical law for the p-Laplacian operator when the two phases agree.

Cited by

• Mixed double phase equations with local and nonlocal operators

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