Rellich inequalities in bounded domains

Abstract

We find necessary and sufficient conditions for the validity of weighted Rellich inequalities in Lp for functions in bounded domains vanishing at the boundary. General operators like L = Delta+ c\|x|^2x nabla-b\|x|^2 are considered. Critical cases and remainder terms are also investigated.

References in corpus (2)

• Gaussian heat kernel upper bounds via Phragmén-Lindelöf theorem
• Regularity of the distance function to the boundary