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
Contributing organizations
Related projects
- Nonlinear Elliptic Equations, Quasiharmonic Fields, and the Range of the Differential
- Jääskeläinen, Jarmo
- Academy of Finland
- InvProbGeomPDE Inverse Problems in Partial Differential Equations and Geometry
- Salo, Mikko
- European Commission
- Nonlinear Problems in Elasticity and Geometric Analysis
- Koski, Aleksis
- Academy of Finland
Ministry reporting: Yes
Reporting Year: 2020
JUFO rating: 3