Eigenvalues for double phase variational integrals

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.

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

References in corpus (1)

• Symmetry in variational principles and applications