Improved Hölder regularity for strongly elliptic PDEs

Kari Astala; Albert Clop; Daniel Faraco; Jarmo Jääskeläinen; Aleksis Koski

doi:10.1016/j.matpur.2020.06.005

Improved Hölder regularity for strongly elliptic PDEs

Kari Astala, Albert Clop, Daniel Faraco^*, Jarmo Jääskeläinen, Aleksis Koski

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

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

1 Citation (Scopus)

Abstract

We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of Hölder regularity, higher than what is given by the classical exponent 1/K.

Original language	English
Pages (from-to)	230-258
Journal	Journal des Mathematiques Pures et Appliquees
Volume	140
Early online date	1 Jan 2020
DOIs	https://doi.org/10.1016/j.matpur.2020.06.005
Publication status	Published - Aug 2020
MoE publication type	A1 Journal article-refereed

Keywords

Beltrami equation
Elliptic equations
Hölder regularity
Quasiconformal mappings

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10.1016/j.matpur.2020.06.005

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title = "Improved H{\"o}lder regularity for strongly elliptic PDEs",

abstract = "We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of H{\"o}lder regularity, higher than what is given by the classical exponent 1/K.",

keywords = "Beltrami equation, Elliptic equations, H{\"o}lder regularity, Quasiconformal mappings",

author = "Kari Astala and Albert Clop and Daniel Faraco and Jarmo J{\"a}{\"a}skel{\"a}inen and Aleksis Koski",

year = "2020",

month = aug,

doi = "10.1016/j.matpur.2020.06.005",

language = "English",

volume = "140",

pages = "230--258",

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T1 - Improved Hölder regularity for strongly elliptic PDEs

AU - Astala, Kari

AU - Clop, Albert

AU - Faraco, Daniel

AU - Jääskeläinen, Jarmo

AU - Koski, Aleksis

PY - 2020/8

Y1 - 2020/8

N2 - We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of Hölder regularity, higher than what is given by the classical exponent 1/K.

AB - We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of Hölder regularity, higher than what is given by the classical exponent 1/K.

KW - Beltrami equation

KW - Elliptic equations

KW - Hölder regularity

KW - Quasiconformal mappings

UR - http://www.scopus.com/inward/record.url?scp=85087214671&partnerID=8YFLogxK

U2 - 10.1016/j.matpur.2020.06.005

DO - 10.1016/j.matpur.2020.06.005

M3 - Article

AN - SCOPUS:85087214671

VL - 140

SP - 230

EP - 258

JO - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

JF - JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES

SN - 0021-7824

ER -

Improved Hölder regularity for strongly elliptic PDEs

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Keywords

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