Aleksandrov's estimates for elliptic equations with drift in Morrey spaces containing $L_{d}$

TL;DR

This paper extends Aleksandrov's maximum principle to elliptic equations with drift coefficients in Morrey spaces containing $L_d$, and with free terms in $L_p$, broadening the applicability of classical estimates.

Contribution

It introduces a version of Aleksandrov's maximum principle for elliptic equations with drifts in Morrey spaces including $L_d$, and free terms in $L_p$, enhancing existing theoretical frameworks.

Findings

Established Aleksandrov's maximum principle in new Morrey space settings.

Extended classical estimates to broader classes of elliptic equations.

Provided conditions under which the maximum principle holds for these equations.

Abstract

In this note, we obtain a version of Aleksandrov's maximum principle when the drift coefficients are in Morrey spaces, which contains $L_d$, and when the free term is in $L_p$ for some $p<d$.