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Zeitschrift für Analysis und ihre Anwendungen


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Volume 13, Issue 1, 1994, pp. 19–47
DOI: 10.4171/ZAA/527

Published online: 1994-03-31

On the Behaviour of Solutions to the Dirichiet Problem for Second Order Elliptic Equations near Edges and Polyhedral Vertices with Critical Angles

Vladimir G. Maz'ya[1] and Jürgen Rossmann[2]

(1) Linköping University, Sweden
(2) Universität Rostock, Germany

The Dirichiet problem for second order elliptic equations will be considered in domains of $\mathbb R^N$ with smooth ($N-2$)-dimensional edges at the boundary. The authors get the asymptotical decomposition of the solution near edges with angles running through a critical value. Furthermore, the first terms of the asymptotics of the solution near a polyhedral vertex are given for a domain with critical angle $\pi$/2 in the vertex.

Keywords: Second order elliptic equations, asymptotics

Maz'ya Vladimir, Rossmann Jürgen: On the Behaviour of Solutions to the Dirichiet Problem for Second Order Elliptic Equations near Edges and Polyhedral Vertices with Critical Angles. Z. Anal. Anwend. 13 (1994), 19-47. doi: 10.4171/ZAA/527