ON SOLVABILITY OF THE NEUMANN PROBLEM IN AN ENERGY SPACE FOR A DOMAIN WITH PEAK

Abstract. We describe the dual space of the boundary trace space for func-tions with a finite Dirichlet integral for a domain with a vertex of an isolated cusp at the boundary. This leads to conditions of solvability of the Neu-mann problem for elliptic equations of second order. In particular, we give an explicit necessary and sufficient condition for q such that the Neumann problem is solvable if the boundary function is in Lq over the boundary of a domain with an outer peak