A1 Journal article (refereed)
Improved Hölder regularity for strongly elliptic PDEs (2020)


Astala, Kari; Clop, Albert; Faraco, Daniel; Jääskeläinen, Jarmo; Koski, Aleksis (2020). Improved Hölder regularity for strongly elliptic PDEs. Journal de Mathematiques Pures et Appliquees, 140, 230-258. DOI: 10.1016/j.matpur.2020.06.005


JYU authors or editors


Publication details

All authors or editors: Astala, Kari; Clop, Albert; Faraco, Daniel; Jääskeläinen, Jarmo; Koski, Aleksis

Journal or series: Journal de Mathematiques Pures et Appliquees

ISSN: 0021-7824

eISSN: 1776-3371

Publication year: 2020

Volume: 140

Pages range: 230-258

Publisher: Elsevier

Publication country: France

Publication language: English

DOI: http://doi.org/10.1016/j.matpur.2020.06.005

Open Access: Publication channel is not openly available

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1906.10906


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.


Keywords: complex analysis; partial differential equations

Free keywords: elliptic equations; quasiconformal mappings; Beltrami equation; Hölder regularity


Contributing organizations


Related projects

Nonlinear Elliptic Equations, Quasiharmonic Fields, and the Range of the Differential
Jääskeläinen, Jarmo
Academy of Finland
01/09/2017-28/02/2018
Nonlinear Problems in Elasticity and Geometric Analysis
Koski, Aleksis
Academy of Finland
01/09/2018-31/08/2021


Ministry reporting: Yes


Last updated on 2020-20-07 at 08:13