H\"older regularity for non divergence form elliptic equations with discontinuous coefficients

TL;DR

This paper investigates the global regularity of second derivatives of solutions to non-divergence form elliptic equations with discontinuous coefficients within Morrey spaces, advancing understanding of solution smoothness under irregular conditions.

Contribution

It provides new results on the regularity of solutions to elliptic equations with discontinuous coefficients in Morrey spaces, a less explored area.

Findings

Established global Morrey space regularity for second derivatives

Extended regularity results to equations with discontinuous coefficients

Improved understanding of solution smoothness in non-divergence form elliptic equations

Abstract

In this note we study the global regularity in the Morrey spaces for the second derivatives for the strong solutions of non variational elliptic equations.