Classical solutions of the divergence equation with Dini-continuous datum

TL;DR

This paper proves the existence of classical solutions to the divergence equation with Dini-continuous data and vanishing boundary conditions, under mild regularity assumptions on the data.

Contribution

It establishes the existence of classical solutions for divergence equations with Dini-continuous data, expanding the understanding of regularity conditions needed.

Findings

Existence of classical solutions under Dini continuity.

Solutions satisfy vanishing Dirichlet boundary conditions.

Results applicable to divergence equations with minimal regularity assumptions.

Abstract

We consider the boundary value problem associated to the divergence operator with vanishing Dirichlet boundary conditions and we prove the existence of classical solutions under slight assumptions on the regularity of the datum.