Optimal Hardy‐weights for elliptic operators with mixed boundary conditions

Abstract

AbstractWe construct families of optimal Hardy‐weights for a subcritical linear second‐order elliptic operator with degenerate mixed boundary conditions. By an optimal Hardy‐weight for a subcritical operator we mean a nonzero nonnegative weight function W such that is critical, and null‐critical with respect to W. Our results rely on a recently developed criticality theory for positive solutions of the corresponding mixed boundary value problem.