Regularity of solutions of the Neumann problem for the Laplace equation

  • Dagmar Medkova

Abstract

Let u be a solution of the Neumann problem for the Laplace equation in G with the boundary condition g. It is shown that uL q (∂ G ) (equivalently, uBq,21/q (G ) for 1 < q ≤ 2, uLq1/q (G ) for 2 ≤ q < ∞) if and only if the single layer potential corresponding to the boundary condition g  is in L q (∂ G ). As a consequence we give a regularity result for some nonlinear boundary value problem.

Published
2007-04-01
Section
Articoli