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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Embedding theorems and quasi-linear elliptic boundary value problems for unbounded domains


Authors: Melvyn S. Berger and Martin Schechter
Journal: Trans. Amer. Math. Soc. 172 (1972), 261-278
MSC: Primary 46E35; Secondary 35J65, 35L60, 49F99
MathSciNet review: 0312241
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Abstract: The Sobolev-Kondrachov embedding and compactness theorems are extended to cover general unbounded domains, by introducing appropriate weighted $ {L_p}$ norms. These results are then applied to the Dirichlet problem for quasi-linear elliptic partial differential equations and isoperimetric variational problems defined on general unbounded domains in $ {{\mathbf{R}}^N}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0312241-X
PII: S 0002-9947(1972)0312241-X
Keywords: $ {L_p}$ embedding, nonlinear eigenvalue problems, isoperimetric problems, critical point theory, quasi-linear elliptic boundary value problems
Article copyright: © Copyright 1972 American Mathematical Society