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

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.

Locations

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