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Embedding Theorems and Quasi-Linear Elliptic Boundary Value Problems for Unbounded Domains

Melvyn S. Berger and Martin Schechter
Transactions of the American Mathematical Society
Vol. 172 (Oct., 1972), pp. 261-278
DOI: 10.2307/1996347
Stable URL: http://www.jstor.org/stable/1996347
Page Count: 18
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Embedding Theorems and Quasi-Linear Elliptic Boundary Value Problems for Unbounded Domains
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Abstract

The Sobolev-Kondrachov embedding and compactness theorems are extended to cover general unbounded domains, by introducing appropriate weighted Lp 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 RN.

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