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

Berger, Melvyn S.; Schechter, Martin

doi:10.1090/S0002-9947-1972-0312241-X

Embedding theorems and quasi-linear elliptic boundary value problems for unbounded domains
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Trans. Amer. Math. Soc. 172 (1972), 261-278 Request permission

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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