Symmetry and compact embeddings for critical exponents in metric-measure spaces

Michał Gaczkowski; Przemysław Górka; Daniel J. Pons

doi:10.1016/j.jde.2020.06.062

Symmetry and compact embeddings for critical exponents in metric-measure spaces

Michał Gaczkowski, Przemysław Górka, Daniel J. Pons

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Abstract

We obtain a compact Sobolev embedding for H-invariant functions in compact metric-measure spaces, where H is a subgroup of the measure preserving bijections. In Riemannian manifolds, H is a subgroup of the volume preserving diffeomorphisms: a compact embedding for the critical exponents follows. The results can be viewed as an extension of Sobolev embeddings of functions invariant under isometries in compact manifolds.

Original language	English
Pages (from-to)	9819-9837
Number of pages	19
Journal	Journal of Differential Equations
Volume	269
Issue number	11
DOIs	https://doi.org/10.1016/j.jde.2020.06.062
Publication status	Published - 15 Nov 2020

Keywords

Compact embedding
Metric-measure spaces
Sobolev spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2020.06.062

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abstract = "We obtain a compact Sobolev embedding for H-invariant functions in compact metric-measure spaces, where H is a subgroup of the measure preserving bijections. In Riemannian manifolds, H is a subgroup of the volume preserving diffeomorphisms: a compact embedding for the critical exponents follows. The results can be viewed as an extension of Sobolev embeddings of functions invariant under isometries in compact manifolds.",

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AU - Gaczkowski, Michał

AU - Górka, Przemysław

AU - Pons, Daniel J.

PY - 2020/11/15

Y1 - 2020/11/15

N2 - We obtain a compact Sobolev embedding for H-invariant functions in compact metric-measure spaces, where H is a subgroup of the measure preserving bijections. In Riemannian manifolds, H is a subgroup of the volume preserving diffeomorphisms: a compact embedding for the critical exponents follows. The results can be viewed as an extension of Sobolev embeddings of functions invariant under isometries in compact manifolds.

AB - We obtain a compact Sobolev embedding for H-invariant functions in compact metric-measure spaces, where H is a subgroup of the measure preserving bijections. In Riemannian manifolds, H is a subgroup of the volume preserving diffeomorphisms: a compact embedding for the critical exponents follows. The results can be viewed as an extension of Sobolev embeddings of functions invariant under isometries in compact manifolds.

KW - Compact embedding

KW - Metric-measure spaces

KW - Sobolev spaces

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M3 - Article

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VL - 269

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EP - 9837

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

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ER -

Symmetry and compact embeddings for critical exponents in metric-measure spaces

Abstract

Keywords

ASJC Scopus subject areas

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