Hölder regularity for degenerate parabolic double-phase equations

Wontae Kim; Kristian Moring; Lauri Särkiö

doi:10.1016/j.jde.2025.113231

Hölder regularity for degenerate parabolic double-phase equations

Wontae Kim^*
, Kristian Moring
, Lauri Särkiö

^*Corresponding author for this work

Paris-Lodron-University of Salzburg

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

5 Citations (Scopus)

121 Downloads (Pure)

Abstract

We prove that bounded weak solutions to degenerate parabolic double-phase equations of p-Laplace type are locally Hölder continuous. The proof is based on phase analysis and methods for the p-Laplace equation. In particular, the phase analysis determines whether the double-phase equation is locally similar to the p-Laplace or the q-Laplace equation.

Original language	English
Article number	113231
Journal	Journal of Differential Equations
Volume	434
DOIs	https://doi.org/10.1016/j.jde.2025.113231
Publication status	Published - 25 Jul 2025
MoE publication type	A1 Journal article-refereed

Keywords

Hölder regularity
Parabolic double-phase equation

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10.1016/j.jde.2025.113231Licence: CC BY

Hölder regularity for degenerate parabolic double-phase equationsFinal published version, 535 KBLicence: CC BY

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title = "H{\"o}lder regularity for degenerate parabolic double-phase equations",

abstract = "We prove that bounded weak solutions to degenerate parabolic double-phase equations of p-Laplace type are locally H{\"o}lder continuous. The proof is based on phase analysis and methods for the p-Laplace equation. In particular, the phase analysis determines whether the double-phase equation is locally similar to the p-Laplace or the q-Laplace equation.",

keywords = "H{\"o}lder regularity, Parabolic double-phase equation",

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T1 - Hölder regularity for degenerate parabolic double-phase equations

AU - Kim, Wontae

AU - Moring, Kristian

AU - Särkiö, Lauri

PY - 2025/7/25

Y1 - 2025/7/25

N2 - We prove that bounded weak solutions to degenerate parabolic double-phase equations of p-Laplace type are locally Hölder continuous. The proof is based on phase analysis and methods for the p-Laplace equation. In particular, the phase analysis determines whether the double-phase equation is locally similar to the p-Laplace or the q-Laplace equation.

AB - We prove that bounded weak solutions to degenerate parabolic double-phase equations of p-Laplace type are locally Hölder continuous. The proof is based on phase analysis and methods for the p-Laplace equation. In particular, the phase analysis determines whether the double-phase equation is locally similar to the p-Laplace or the q-Laplace equation.

KW - Hölder regularity

KW - Parabolic double-phase equation

UR - https://www.scopus.com/pages/publications/105000066319

U2 - 10.1016/j.jde.2025.113231

DO - 10.1016/j.jde.2025.113231

M3 - Article

AN - SCOPUS:105000066319

SN - 0022-0396

VL - 434

JO - Journal of Differential Equations

JF - Journal of Differential Equations

M1 - 113231

ER -

Hölder regularity for degenerate parabolic double-phase equations

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Keywords

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