Poincare Inequalities and Neumann Problems for the p-Laplacian

2017/08/13 by Cruz-Uribe, David, Rodney, Scott, Rosta, Emily · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.03932

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.

Cited by

• The weak maximum principle for solutions of degenerate elliptic equations with lower order terms
• Existence and uniqueness of solutions of degenerate elliptic equations with lower order terms

Related

• Poincar 'e Inequalities and Neumann Problems for the Variable Exponent\n Setting
• Matrix weighted Poincaré inequalities and applications to degenerate elliptic systems
• Eigenvalues of the Neumann Laplacian with density and sharp Sobolev-Orlicz embeddings
• Degenerate Poincaré-Sobolev inequalities
• An inequality à la Szegő-Weinberger for the p-Laplacian on convex sets