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Bitte nutzen Sie beim Zitieren immer folgende Url:

http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601506

Kurzfassung in Englisch

The solutions to certain elliptic boundary value
problems have singularities with a typical
structure near polyhedral corners. This structure
can be exploited to devise an eigenvalue problem
whose solution can be used to quantify the
singularities of the given boundary value problem.
It is necessary to parametrize a ball centered at
the corner. There are different possibilities for
a suitable parametrization; from the numerical
point of view, spherical coordinates are not
necessarily the best choice. This is why we do
not specify a parametrization in this paper but
present all results in a rather general form.
We derive the eigenvalue problems that are
associated with the Laplace and the linear
elasticity problems and show interesting
spectral properties. Finally, we discuss the
necessity of widely accepted symmetry properties
of the elasticity tensor. We show in an example
that some of these properties are not only
dispensable, but even invalid, although claimed
in many standard books on linear elasticity.

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