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General edge asymptotics of solutions of second-order elliptic boundary value problems. II. (English) Zbl 0791.35033

Author’s abstract: This is the second of two papers (see above) in which we study the singularities of solutions of second-order linear elliptic boundary value problems at the edges of piecewise analytic domains in \(\mathbb{R}^ 3\). When the opening angle at the edge is variable, there appears the phenomenon of “crossing” of the exponents of singualrities. In Part I, we introduced for the Dirichlet problem appropriate combinations of the simple tensor product singularities.
In this second part, we extend the result of Part I to general non- homogeneous boundary conditions. Moreover, we show how these combinations of singularities appear in a natural way as sections of an analytic vector bundle above the edge. In the case when the interior operator is the Laplacian, we give a simpler expression of the combined singular functions, involving divided differences of powers of a complex variable describing the coordinates in the normal plane to the edge.
Reviewer: H.Ding (Beijing)

MSC:

35J25 Boundary value problems for second-order elliptic equations
35A20 Analyticity in context of PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs

Citations:

Zbl 0791.35034
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References:

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