Sobolev spaces with variable exponents on complete manifolds

Michał Gaczkowski, Przemysław Górka, Daniel J. Pons

Resultado de la investigación: Article

5 Citas (Scopus)

Resumen

We study variable exponent function spaces on complete non-compact Riemannian manifolds. Using classic assumptions on the geometry, continuous embeddings between Sobolev and Hölder function spaces are obtained. We prove compact embeddings of H-invariant Sobolev spaces, where H is a compact Lie subgroup of the group of isometries of the manifold. As an application, we prove the existence of non-trivial solutions to non-homogeneous q(x)-Laplace equations.

Idioma originalEnglish
Páginas (desde-hasta)1379-1415
Número de páginas37
PublicaciónJournal of Functional Analysis
Volumen270
N.º4
DOI
EstadoPublished - 15 feb 2016

Huella dactilar

Variable Exponent
Function Space
Sobolev Spaces
Compact Embedding
Noncompact Manifold
Nontrivial Solution
Laplace's equation
Isometry
Riemannian Manifold
Subgroup
Invariant

ASJC Scopus subject areas

  • Analysis

Citar esto

Gaczkowski, Michał ; Górka, Przemysław ; Pons, Daniel J. / Sobolev spaces with variable exponents on complete manifolds. En: Journal of Functional Analysis. 2016 ; Vol. 270, N.º 4. pp. 1379-1415.
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Sobolev spaces with variable exponents on complete manifolds. / Gaczkowski, Michał; Górka, Przemysław; Pons, Daniel J.

En: Journal of Functional Analysis, Vol. 270, N.º 4, 15.02.2016, p. 1379-1415.

Resultado de la investigación: Article

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AU - Górka, Przemysław

AU - Pons, Daniel J.

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Y1 - 2016/2/15

N2 - We study variable exponent function spaces on complete non-compact Riemannian manifolds. Using classic assumptions on the geometry, continuous embeddings between Sobolev and Hölder function spaces are obtained. We prove compact embeddings of H-invariant Sobolev spaces, where H is a compact Lie subgroup of the group of isometries of the manifold. As an application, we prove the existence of non-trivial solutions to non-homogeneous q(x)-Laplace equations.

AB - We study variable exponent function spaces on complete non-compact Riemannian manifolds. Using classic assumptions on the geometry, continuous embeddings between Sobolev and Hölder function spaces are obtained. We prove compact embeddings of H-invariant Sobolev spaces, where H is a compact Lie subgroup of the group of isometries of the manifold. As an application, we prove the existence of non-trivial solutions to non-homogeneous q(x)-Laplace equations.

KW - Lebesgue spaces with variable exponents

KW - Riemannian manifolds

KW - Sobolev spaces

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