Abstract
The asymptotics of the solution of the Neumann problem is studied for a second-order elliptic equation near a point of tangency of two surfaces forming the boundary of a domain in Rn, n≥3. In accordance with the procedure of investigating problems in thin domains, the resulting equation is found on the hyperplane Rn–1, the power solutions of which occur in the asymptotics. The justification of the expansion first found formally is based on a priori estimates of solutions in spaces with weighted norms, reduction of the problem to the resulting equation by means of integration, and application of a familiar theorem regarding the asymptotics of the latter.
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