Eigenvalues of Elliptic Systems for the Mixed Problem in Perturbations of Lipschitz Domains with Nonhomogeneous Neumann Boundary Conditions

Abstract

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We study eigenvalues of an elliptic operator with mixed boundary \nconditions on very general decompositions of the boundary. We impose \nnonhomogeneous\nconditions on the part of the boundary where the Neumann term lies in a \ncertain\nSobolev or $L^p$ space. Our work compares the behavior of and gives a relationship\nbetween the eigenvalues and eigenfunctions on the unperturbed and perturbed domains, respectively.<\/p>"