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Höppner, Wolfgang [Author]; Ziegler, Günter [Author]; Kaiser, Hans-Christoph [Author]; Rehberg, Joachim [Author]; Haller-Dintelmann, Robert [Author]

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

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  • Media type: Text; E-Article
  • Title: Optimal elliptic Sobolev regularity near three-dimensional multi-material Neumann vertices
  • Contributor: Höppner, Wolfgang [Author]; Ziegler, Günter [Author]; Kaiser, Hans-Christoph [Author]; Rehberg, Joachim [Author]; Haller-Dintelmann, Robert [Author]
  • Published: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2014
  • Language: English
  • DOI: https://doi.org/10.1007/s10688-014-0062-z
  • ISSN: 1573-8485 -- 0016-2663 -- Funct. Anal. Appl. -- Functional Analysis and Its Applications -- 2037147-0 -- https://www.springer.com/journal/10688
  • Keywords: Elliptic div-grad operators -- anisotropic ellipticity in three dimensions -- transmission at material interfaces -- mixed Dirichlet--Neumann boundary conditions -- optimal Sobolev regularity ; article
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  • Description: We study the 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 part of the boundary of a 3D polyhedral domain. The gradient of any solution of the corresponding elliptic partial differential equation (in a neighborhood of the vertex) is p-integrable with p > 3.