A boundary estimate for singular parabolic diffusion equations

Ugo Gianazza; Naian Liao; Teemu Lukkari

doi:10.1007/s00030-018-0523-9

A boundary estimate for singular parabolic diffusion equations

Ugo Gianazza^*, Naian Liao, Teemu Lukkari

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

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

Abstract

We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of p-Laplacian type. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic p-capacity.

Original language	English
Article number	33
Number of pages	24
Journal	NODEA: NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
Volume	25
Issue number	4
DOIs	https://doi.org/10.1007/s00030-018-0523-9
Publication status	Published - Aug 2018
MoE publication type	A1 Journal article-refereed

Keywords

Parabolic p-Laplacian
Boundary estimates
Continuity
Elliptic p-capacity
Wiener-type integral
WEAK SUPERSOLUTIONS
DEGENERATE
REGULARITY

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title = "A boundary estimate for singular parabolic diffusion equations",

abstract = "We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of p-Laplacian type. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic p-capacity.",

keywords = "Parabolic p-Laplacian, Boundary estimates, Continuity, Elliptic p-capacity, Wiener-type integral, WEAK SUPERSOLUTIONS, DEGENERATE, REGULARITY",

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T1 - A boundary estimate for singular parabolic diffusion equations

AU - Gianazza, Ugo

AU - Liao, Naian

AU - Lukkari, Teemu

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N2 - We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of p-Laplacian type. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic p-capacity.

AB - We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of p-Laplacian type. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic p-capacity.

KW - Parabolic p-Laplacian

KW - Boundary estimates

KW - Continuity

KW - Elliptic p-capacity

KW - Wiener-type integral

KW - WEAK SUPERSOLUTIONS

KW - DEGENERATE

KW - REGULARITY

U2 - 10.1007/s00030-018-0523-9

DO - 10.1007/s00030-018-0523-9

M3 - Article

VL - 25

JO - NODEA: NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS

JF - NODEA: NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS

SN - 1021-9722

IS - 4

M1 - 33

ER -

A boundary estimate for singular parabolic diffusion equations

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Keywords

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