Optimal elliptic Sobolev regularity near three-dimensional, multi-material Neumann vertices

Please always quote using this URN: urn:nbn:de:0296-matheon-8083
  • We investigate optimal elliptic regularity (within the scale of Sobolev spaces) of anisotropic div--grad operators in three dimensions at a multi-material vertex on the Neumann boundary part of a polyhedral spatial domain. The gradient of a solution to the corresponding elliptic PDE (in a neighbourhood of the vertex) is integrable to an index greater than three.
  • On considère des opérateurs div-grad dans un polyèdre en trois dimensions avec des conditions aux bords de Neumann. Dans l'échelle des espaces de Sobolev on s'intéresse à la régularité optimale elliptique proche d'un sommet dans lequelle des matériaux différents sont présent. On montre que (dans un voisinage du sommet) le gradient de la solution de l'EDP correspondante est intégrable avec un exposant supérieur à trois.

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Metadaten
Author:Robert Haller-Dintelmann, Wolfgang Höppner, Hans-Christoph Kaiser , Günter M. Ziegler
URN:urn:nbn:de:0296-matheon-8083
Referee:Peter Deuflhard
Language:English
Date of first Publication:2011/04/22
Institute:Research Center Matheon
Freie Universität Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Dxx Generalized solutions / 35D30 Weak solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J25 Boundary value problems for second-order elliptic equations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Rxx Miscellaneous topics (For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDE, see also 60H15) / 35R05 Partial differential equations with discontinuous coefficients or data
57-XX MANIFOLDS AND CELL COMPLEXES (For complex manifolds, see 32Qxx) / 57Qxx PL-topology / 57Q25 Comparison of PL-structures: classification, Hauptvermutung
Preprint Number:777

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