On Hölder regularity for elliptic equations of non-divergence type in the plane

Albert Baernstein, Leonid V. Kovalev

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

This paper is concerned with strong solutions of uniformly elliptic equations of non-divergence type in the plane. First, we use the notion of quasiregular gradient mappings to improve Morrey's theorem on the Hölder continuity of gradients of solutions. Then we show that the Gilbarg-Serrin equation does not produce the optimal Hölder exponent in the considered class of equations. Finally, we propose a conjecture for the best possible exponent and prove it under an additional restriction.

Original languageEnglish (US)
Pages (from-to)295-317
Number of pages23
JournalAnnali della Scuola Normale - Classe di Scienze
Volume4
Issue number2
StatePublished - Dec 1 2005
Externally publishedYes

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)

Fingerprint Dive into the research topics of 'On Hölder regularity for elliptic equations of non-divergence type in the plane'. Together they form a unique fingerprint.

  • Cite this