H\"older regularity of solutions for Schr\"odinger operators on stratified spaces

TL;DR

This paper investigates the regularity of solutions to Schr"odinger equations on stratified spaces with edge metrics, establishing optimal H"older regularity under minimal assumptions.

Contribution

It provides new results on the H"older regularity of Schr"odinger solutions on stratified spaces with minimal metric and potential conditions.

Findings

Solutions exhibit optimal H"older regularity.

Regularity results hold under minimal assumptions.

Applicable to Schr"odinger equations on complex stratified geometries.

Abstract

We study the regularity properties for solutions of a class of Schr\"odinger equations $(\Delta + V) u = 0$ on a stratified space $M$ endowed with an iterated edge metric. The focus is on obtaining optimal H\"older regularity of these solutions assuming fairly minimal conditions on the underlying metric and potential.