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This article is cited in 4 scientific papers (total in 4 papers)
Optimal Elliptic Sobolev Regularity Near Three-Dimensional Multi-Material Neumann Vertices
R. Haller-Dintelmanna, W. Höppnerb, H.-Ch. Kaiserb, J. Rehbergb, G. M. Zieglerc a Technische Universität Darmstadt
b Weierstrass-Institut für Angewandte Analysis und Stochastik, Berlin
c Freie Universität Berlin
Abstract:
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 $p>3$.
Keywords:
elliptic div–grad operator, piecewise linear 3D flattening, anisotropic ellipticity in three dimensions, transmission at
material interfaces, mixed Dirichlet–Neumann boundary conditions, optimal Sobolev regularity.
Received: 31.01.2012
Citation:
R. Haller-Dintelmann, W. Höppner, H.-Ch. Kaiser, J. Rehberg, G. M. Ziegler, “Optimal Elliptic Sobolev Regularity Near Three-Dimensional Multi-Material Neumann Vertices”, Funktsional. Anal. i Prilozhen., 48:3 (2014), 63–83; Funct. Anal. Appl., 48:3 (2014), 208–222
Linking options:
https://www.mathnet.ru/eng/faa3152https://doi.org/10.4213/faa3152 https://www.mathnet.ru/eng/faa/v48/i3/p63
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Abstract page: | 434 | Full-text PDF : | 176 | References: | 68 | First page: | 26 |
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