Hölder continuity for Trudinger's equation in measure spaces

Tuomo Kuusi; Rojbin Laleoglu; Juhana Siljander; José Miguel Urbano

doi:10.1007/s00526-011-0456-1

Hölder continuity for Trudinger's equation in measure spaces

Tuomo Kuusi, Rojbin Laleoglu, Juhana Siljander, José Miguel Urbano

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

We complete the study of the regularity for Trudinger's equation by proving that weak solutions are Hölder continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincaré inequality. The proof uses the Harnack inequality and intrinsic scaling. © 2011 Springer-Verlag.

Original language	English (US)
Pages (from-to)	193-229
Number of pages	37
Journal	Calculus of Variations and Partial Differential Equations
Volume	45
Issue number	1-2
DOIs	https://doi.org/10.1007/s00526-011-0456-1
State	Published - Sep 1 2012
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

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AB - We complete the study of the regularity for Trudinger's equation by proving that weak solutions are Hölder continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincaré inequality. The proof uses the Harnack inequality and intrinsic scaling. © 2011 Springer-Verlag.

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Hölder continuity for Trudinger's equation in measure spaces

Abstract

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