Poincare Inequalities and Neumann Problems for the p-Laplacian

Abstract

We prove an equivalence between weighted Poincare inequalities and the existence of weak solutions to a Neumann problem related to a degenerate p- Laplacian. The Poincare inequalities are formulated in the context of degenerate Sobolev spaces defined in terms of a quadratic form, and the associated matrix is the source of the degeneracy in the p-Laplacian.

References in corpus (1)

• Two weight norm inequalities for fractional integral operators and commutators

Cited by in corpus (1)

• Two weight bump conditions for matrix weights