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We study eigenvalues of an elliptic operator with mixed boundary conditions on very general decompositions of the boundary. We impose nonhomogeneous conditions on the part of the boundary where the Neumann term lies in a certain Sobolev or $L^p$ space. Our work compares the behavior of and gives a relationship between the eigenvalues and eigenfunctions on the unperturbed and perturbed domains, respectively.
}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v33.n1.4}, url = {http://global-sci.org/intro/article_detail/jpde/15803.html} }We study eigenvalues of an elliptic operator with mixed boundary conditions on very general decompositions of the boundary. We impose nonhomogeneous conditions on the part of the boundary where the Neumann term lies in a certain Sobolev or $L^p$ space. Our work compares the behavior of and gives a relationship between the eigenvalues and eigenfunctions on the unperturbed and perturbed domains, respectively.