WIAS Preprint No. 1515, (2010)

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



Authors

  • Haller-Dintelmann, Robert
  • Höppner, Wolfgang
  • Kaiser, Hans-Christoph
  • Rehberg, Joachim
  • Ziegler, Günter

2010 Mathematics Subject Classification

  • 35D10 35J25 35R05 57Q25

Keywords

  • Elliptic div-grad operators, anisotropic ellipticity in three dimensions, transmission at material interfaces, mixed Dirichlet--Neumann boundary conditions, optimal Sobolev regularity

Abstract

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 the 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.

Appeared in

  • Funct. Anal. Appl., 48 (2014) pp. 208--222. Primary publication: ``Optimal'naya ellipticheskaya regulyarnost' v prostranstvakh Soboleva vblizi tryokhmernykh mnogomaterial'nykh vershin Neumana'' (Russian) in ``Funktsional'nyi Analiz i Ego Prilozheniya'', Vol. 48, No. 3, pp. 63--83, 2014

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