Higher integrability for doubly nonlinear parabolic systems

Verena Boegelein; Frank Duzaar; Juha Kinnunen; Christoph Scheven

doi:10.1016/j.matpur.2020.06.009

Higher integrability for doubly nonlinear parabolic systems

Verena Boegelein, Frank Duzaar, Juha Kinnunen, Christoph Scheven^*

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

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

14 Citations (Scopus)

Abstract

This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the intrinsic geometry involves the solution as well as its spatial gradient. The main result holds true for a range of parameters suggested by other nonlinear parabolic systems.

Original language	English
Pages (from-to)	31-72
Number of pages	42
Journal	Journal de Mathematiques Pures et Appliquees
Volume	143
DOIs	https://doi.org/10.1016/j.matpur.2020.06.009
Publication status	Published - Nov 2020
MoE publication type	A1 Journal article-refereed

Keywords

Doubly nonlinear parabolic equation
Higher integrability
Gradient estimates
Intrinsic geometry
DIFFUSIVE WAVE APPROXIMATION
LOCAL HOLDER CONTINUITY
SELF-IMPROVING PROPERTY
WEAK SOLUTIONS
GRADIENT
BOUNDEDNESS
REGULARITY
EQUATIONS
BEHAVIOR

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title = "Higher integrability for doubly nonlinear parabolic systems",

abstract = "This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the intrinsic geometry involves the solution as well as its spatial gradient. The main result holds true for a range of parameters suggested by other nonlinear parabolic systems.",

keywords = "Doubly nonlinear parabolic equation, Higher integrability, Gradient estimates, Intrinsic geometry, DIFFUSIVE WAVE APPROXIMATION, LOCAL HOLDER CONTINUITY, SELF-IMPROVING PROPERTY, WEAK SOLUTIONS, GRADIENT, BOUNDEDNESS, REGULARITY, EQUATIONS, BEHAVIOR",

author = "Verena Boegelein and Frank Duzaar and Juha Kinnunen and Christoph Scheven",

year = "2020",

month = nov,

doi = "10.1016/j.matpur.2020.06.009",

language = "English",

volume = "143",

pages = "31--72",

journal = "JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES",

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T1 - Higher integrability for doubly nonlinear parabolic systems

AU - Boegelein, Verena

AU - Duzaar, Frank

AU - Kinnunen, Juha

AU - Scheven, Christoph

PY - 2020/11

Y1 - 2020/11

N2 - This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the intrinsic geometry involves the solution as well as its spatial gradient. The main result holds true for a range of parameters suggested by other nonlinear parabolic systems.

AB - This paper proves a local higher integrability result for the spatial gradient of weak solutions to doubly nonlinear parabolic systems. The new feature of the argument is that the intrinsic geometry involves the solution as well as its spatial gradient. The main result holds true for a range of parameters suggested by other nonlinear parabolic systems.

KW - Doubly nonlinear parabolic equation

KW - Higher integrability

KW - Gradient estimates

KW - Intrinsic geometry

KW - DIFFUSIVE WAVE APPROXIMATION

KW - LOCAL HOLDER CONTINUITY

KW - SELF-IMPROVING PROPERTY

KW - WEAK SOLUTIONS

KW - GRADIENT

KW - BOUNDEDNESS

KW - REGULARITY

KW - EQUATIONS

KW - BEHAVIOR

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DO - 10.1016/j.matpur.2020.06.009

M3 - Article

VL - 143

SP - 31

EP - 72

JO - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

JF - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

SN - 0021-7824

ER -

Higher integrability for doubly nonlinear parabolic systems

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Keywords

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