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We describe the dual space of the boundary trace space for functions 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 Neumann problem for elliptic equations of second order. In particular, we give an explicit necessary and sufficient condition for  such that the Neumann problem is solvable if the boundary function is in    over the boundary of a domain with an outer peak.

On Solvability of the Neumann Problem in an Energy Space for a Domain with Peak