The $C^{\a}$ regularity of a class of non-homogeneous ultraparabolic equations

TL;DR

This paper establishes $C^{eta}$ regularity for weak solutions of a broad class of non-homogeneous ultraparabolic equations with measurable coefficients, extending previous results for homogeneous cases.

Contribution

It generalizes existing $C^{eta}$ regularity results from homogeneous to non-homogeneous ultraparabolic equations with measurable coefficients.

Findings

Proves $C^{eta}$ regularity for weak solutions

Extends regularity results to non-homogeneous equations

Handles measurable coefficients in ultraparabolic equations

Abstract

We obtain the $C^{\a}$ regularity for weak solutions of a class of non-homogeneous ultraparabolic equation, with measurable coefficients. The result generalizes our recent $C^{\a}$ regularity results of homogeneous ultraparabolic equation.