Local Hölder continuity for doubly nonlinear parabolic equations

Tuomo Kuusi; Juhana Siljander; José Miguel Urbano

doi:10.1512/iumj.2012.61.4513

Local Hölder continuity for doubly nonlinear parabolic equations

Tuomo Kuusi, Juhana Siljander, José Miguel Urbano

Department of Mathematics and Systems Analysis

University of Coimbra

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

30 Citations (Scopus)

Abstract

We give a proof of the Hölder continuity of weak solutions of certain degenerate doubly nonlinear parabolic equations in measure spaces. We only assume the measure to be a doubling nontrivial Borel measure which supports a Poincaré inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, which require intrinsic scaling methods.

Original language	English
Pages (from-to)	399-430
Number of pages	32
Journal	Indiana University Mathematics Journal
Volume	61
Issue number	1
DOIs	https://doi.org/10.1512/iumj.2012.61.4513
Publication status	Published - 2012
MoE publication type	A1 Journal article-refereed

Keywords

Caccioppoli estimates
Harnack's inequality
Hölder continuity
Intrinsic scaling

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10.1512/iumj.2012.61.4513

Cite this

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abstract = "We give a proof of the H{\"o}lder continuity of weak solutions of certain degenerate doubly nonlinear parabolic equations in measure spaces. We only assume the measure to be a doubling nontrivial Borel measure which supports a Poincar{\'e} inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, which require intrinsic scaling methods.",

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AB - We give a proof of the Hölder continuity of weak solutions of certain degenerate doubly nonlinear parabolic equations in measure spaces. We only assume the measure to be a doubling nontrivial Borel measure which supports a Poincaré inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, which require intrinsic scaling methods.

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KW - Intrinsic scaling

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Local Hölder continuity for doubly nonlinear parabolic equations

Abstract

Keywords

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