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.
Colasuonno, F., Squassina, M., Eigenvalues for double phase variational problems, <<ANNALI DI MATEMATICA PURA ED APPLICATA>>, 2016; 195 (6): 1917-1959. [doi:10.1007/s10231-015-0542-7] [http://hdl.handle.net/10807/87019]
Eigenvalues for double phase variational problems
Squassina, MarcoUltimo
2016
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.
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