H\"older regularity of solutions for Schr\"odinger operators on   stratified spaces
  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. 
Kazuo Akutagawa, Gilles Carron (LMJL), Rafe Mazzeo
math.DG