Hölder regularity of solutions for Schrödinger operators on stratified spaces

Kazuo Akutagawa (1) , Gilles Carron (2) , Rafe Mazzeo (3)

1 Department of Mathematics
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 Department of Mathematics

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

Domaines: Géométrie différentielle [math.DG]

Kazuo Akutagawa, Gilles Carron, Rafe Mazzeo. Hölder regularity of solutions for Schrödinger operators on stratified spaces. Journal of Functional Analysis, 2015, 269 (3), pp.815--840. ⟨hal-01059372⟩