The L^p Boundary Value Problems on Lipschitz Domains

Abstract

We develop a new approach to the invertibility of the layer potentials on $L^p$ associated with elliptic equations and systems in Lipschitz domains. As a consequence, for $n\ge 4$ and $(2(n-1)/(n+1))-\epsilon <p<2$, we obtain the solvability of the L^p Neumann type boundary value problems for second order elliptic systems. The analogous results for the biharmonic equation are also established.

Cited by in corpus (5)

• The mixed problem for the Laplacian in Lipschitz domains
• Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity
• The mixed problem for the Lamé system in two dimensions
• Estimates for Green functions of Stokes systems in two dimensional domains
• The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions