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

Jääskeläinen, Jarmo

Koski, Aleksis

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

Fields of science:

111 Mathematics (Natural sciences)