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Volume 33, Issue 1
Eigenvalues of Elliptic Systems for the Mixed Problem in Perturbations of Lipschitz Domains with Nonhomogeneous Neumann Boundary Conditions

Kohei Miyazaki & Justin L. Taylor

DOI: 10.4208/jpde.v33.n1.4

J. Part. Diff. Eq., 33 (2020), pp. 48-63.

Published online: 2020-03

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  • Abstract

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.

  • Keywords

Eigenvalues, elliptic systems, mixed problem, perturbed domains.

  • AMS Subject Headings

35A23, 35B65, 35D30, 35J57, 35M32, 35P99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

kmiyazaki@murraystate.edu (Kohei Miyazaki)

jtaylor52@murraystate.edu (Justin L. Taylor)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-33-48, author = {Miyazaki , Kohei and Taylor , Justin L.}, title = {Eigenvalues of Elliptic Systems for the Mixed Problem in Perturbations of Lipschitz Domains with Nonhomogeneous Neumann Boundary Conditions}, journal = {Journal of Partial Differential Equations}, year = {2020}, volume = {33}, number = {1}, pages = {48--63}, abstract = {

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} }
TY - JOUR T1 - Eigenvalues of Elliptic Systems for the Mixed Problem in Perturbations of Lipschitz Domains with Nonhomogeneous Neumann Boundary Conditions AU - Miyazaki , Kohei AU - Taylor , Justin L. JO - Journal of Partial Differential Equations VL - 1 SP - 48 EP - 63 PY - 2020 DA - 2020/03 SN - 33 DO - http://doi.org/10.4208/jpde.v33.n1.4 UR - https://global-sci.org/intro/article_detail/jpde/15803.html KW - Eigenvalues, elliptic systems, mixed problem, perturbed domains. AB -

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.

Miyazaki , Kohei and Taylor , Justin L.. (2020). Eigenvalues of Elliptic Systems for the Mixed Problem in Perturbations of Lipschitz Domains with Nonhomogeneous Neumann Boundary Conditions. Journal of Partial Differential Equations. 33 (1). 48-63. doi:10.4208/jpde.v33.n1.4
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