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Über die Asymptotik der Lösungen elliptischer Randwertaufgaben in der Umgebung von Kanten. (On the asymptotic representation of solutions of elliptic boundary value problems in the neighbourhood of angles). (German) Zbl 0672.35020
This is a summary of the authors’ recent work [see their preprints, Akad. Wiss. DDR, Inst. Math. P.-Math-07/84, 50 p. (1984; Zbl 0547.35042)] on the analytical properties of the solutions to elliptic boundary value problems in bounded n-dimensional domains which are in a neighborhood of an (n-2)-dimensional submanifold diffeomorphic to a dihedral angle. The right-hand sides of the equation and of the (differential) boundary conditions are assumed to be elements of weighted Sobolev spaces (where - as usual - the weight depends on the distance from the edge), thus the solution is found in a space of such kind, too. Based on the study of weighted spaces in a dihedral angle (particular of the traces of the functions), the authors give the regularity properties of the solution. Special attention is given to asymptotic representations of the solution in the angle and in the domain, containing explicit terms which depend algebraically and logarithmically on the distance from the edge. New results under weaker assumptions for the right-hand sides are included.
Reviewer: E.Lanckau

MSC:
35J40 Boundary value problems for higher-order elliptic equations
35C20 Asymptotic expansions of solutions to PDEs
35D10 Regularity of generalized solutions of PDE (MSC2000)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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