Classical solutions for the system ${\text{curl}\,v=g}$, with vanishing Dirichlet boundary conditions

TL;DR

This paper establishes the existence of classical solutions for the curl boundary value problem with zero Dirichlet conditions under mild data regularity assumptions.

Contribution

It provides a rigorous proof of classical solutions' existence for the curl system with boundary conditions, expanding the understanding of such PDEs.

Findings

Existence of classical solutions under mild regularity conditions

Boundary value problem for curl operator with Dirichlet conditions solved

Theoretical framework for curl boundary problems developed

Abstract

We consider the boundary value problem associated to the curl operator, with vanishing Dirichlet boundary conditions. We prove, under mild regularity of the data of the problem, existence of classical solutions.