Solution of the Dirichlet and Neumann problems for a modified Helmholtz equation in Besov spaces on an annulus

Abstract

Here we study Dirichlet and Neumann problems for a special Helmholtz equation on an annulus. Our main aim is to measure smoothness of solutions for the boundary datum in Besov spaces. We shall use operator theory to solve this problem. The most important advantage of this technique is that it enables to consider equations in vector-valued settings. It is interesting to note that optimal regularity of this problem will be a special case of our main result. (C) 2010 Elsevier Inc. All rights reserved.