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

Astala, K., Clop, A., Faraco, D., Jääskeläinen, J., & Koski, A. (2020). Improved Hölder regularity for strongly elliptic PDEs. Journal de Mathematiques Pures et Appliquees, 140, 230-258. https://doi.org/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: https://doi.org/10.1016/j.matpur.2020.06.005

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://research.aalto.fi/en/publications/improved-h%C3%B6lder-regularity-for-strongly-elliptic-pdes

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

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Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 3