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Stability for the Dirichlet Problem under Continuous Steiner Symmetrization (2000)

Bucur, Dorin ; Henrot, Antoine

Springer

Potential analysis 13 (2000), S. 127-145

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ISSN: 1572-929X

Keywords: Continuous Steiner symmetrization ; Dirichlet problem ; eigenvalues

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract In this paper we prove the existence of a deformation transforming an arbitrary open set into the ball, which has the following properties: it keeps constant the measure, the kth eigenvalue of Laplace–Dirichlet operator is continuous from the left and the first eigenvalue is decreasing. The deformation is given by a sequence of continuous Steiner symmetrizations, and the behavior of the eigenvalues is related to the stability of the Dirichlet problem.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1008753703185

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