Improved Hölder regularity for strongly elliptic PDEs

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

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-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 languageEnglish
Pages (from-to)230-258
JournalJournal des Mathematiques Pures et Appliquees
Volume140
Early online date1 Jan 2020
DOIs
Publication statusPublished - Aug 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Beltrami equation
  • Elliptic equations
  • Hölder regularity
  • Quasiconformal mappings

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