Sobolev spaces with variable exponents on Riemannian manifolds

Sobolev spaces with variable exponents on Riemannian manifolds

In this article we study variable exponent Sobolev spaces on Riemannian manifolds. The spaces are examined in the case of compact manifolds. Continuous and compact embeddings are discussed. The paper contains an example of the application of the theory to elliptic equations on compact manifolds.

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Veröffentlicht in:Nonlinear analysis 2013-11, Vol.92, p.47-59
Hauptverfasser: Gaczkowski, Michał, Górka, Przemysław
Format: Artikel
Sprache:eng
Schlagworte:
Exponents
Lebesgue spaces with variable exponents
Manifolds
Mathematical analysis
Nonlinearity
Riemannian manifolds
Sobolev space
Sobolev spaces
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Zusammenfassung:In this article we study variable exponent Sobolev spaces on Riemannian manifolds. The spaces are examined in the case of compact manifolds. Continuous and compact embeddings are discussed. The paper contains an example of the application of the theory to elliptic equations on compact manifolds.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2013.06.012