On the study of the wave equation set on a singular cylindrical domain

TL;DR

This paper investigates the regularity of solutions to the wave equation in a singular cylindrical domain, introducing new results in anisotropic Hölder spaces under various boundary conditions.

Contribution

It provides novel regularity results for the wave equation on nonsmooth domains using anisotropic Hölder spaces, expanding understanding of boundary effects.

Findings

Established new regularity results for solutions.

Analyzed effects of boundary conditions on solution smoothness.

Extended theory to nonsmooth, singular domains.

Abstract

In this work we give new regularity results of solutions for the linear wave equation set in a nonsmooth cylindrical domain. Different types of conditions are imposed on the boundary of the singular domain. Our study is performed in some particular anisotropic H\"{o}lder spaces.