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

^*Tämän työn vastaava kirjoittaja

Paris-Lodron-University Salzburg

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

1 Sitaatiot (Scopus)

5 Lataukset (Pure)

Abstrakti

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.

Alkuperäiskieli	Englanti
Artikkeli	113231
Julkaisu	Journal of Differential Equations
Vuosikerta	434
DOI - pysyväislinkit	https://doi.org/10.1016/j.jde.2025.113231
Tila	Julkaistu - 25 heinäk. 2025
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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10.1016/j.jde.2025.113231Lisenssi: CC BY

Hölder regularity for degenerate parabolic double-phase equationsFinal published version, 535 KBLisenssi: 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",

author = "Wontae Kim and Kristian Moring and Lauri S{\"a}rki{\"o}",

note = "Publisher Copyright: {\textcopyright} 2025 The Author(s)",

year = "2025",

month = jul,

day = "25",

doi = "10.1016/j.jde.2025.113231",

language = "English",

volume = "434",

journal = "Journal of Differential Equations",

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TY - JOUR

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 - http://www.scopus.com/inward/record.url?scp=105000066319&partnerID=8YFLogxK

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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