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Funktsional'nyi Analiz i ego Prilozheniya, 2014, Volume 48, Issue 3, Pages 63–83
DOI: https://doi.org/10.4213/faa3152 (Mi faa3152) 		 
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
Full-text PDF (291 kB) Citations (4)
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DOI: https://doi.org/10.4213/faa3152
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.
Funding agency Grant number
Forschungszentrum Matheon
European Research Council 247029-SDModels
Received: 31.01.2012
English version:
Functional Analysis and Its Applications, 2014, Volume 48, Issue 3, Pages 208–222
DOI: https://doi.org/10.1007/s10688-014-0062-z
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    1. ter Elst A.F.M., Rehberg J., “Consistent operator semigroups and their interpolation”, J. Operat. Theor., 82:1 (2019), 3–21  crossref  mathscinet  isi  scopus
    2. D. Horstmann, H. Meinlschmidt, J. Rehberg, “The full Keller-Segel model is well-posed on nonsmooth domains”, Nonlinearity, 31:4 (2018), 1560–1592  crossref  mathscinet  zmath  isi  scopus
    3. H. Meinlschmidt, C. Meyer, J. Rehberg, “Optimal control of the thermistor problem in three spatial dimensions, Part 1: Existence of optimal solutions”, SIAM J. Control Optim., 55:5 (2017), 2876–2904  crossref  mathscinet  zmath  isi
    4. K. Disser, H.-Ch. Kaiser, J. Rehberg, “Optimal Sobolev regularity for linear second-order divergence elliptic operators occurring in real-world problems”, SIAM J. Math. Anal., 47:3 (2015), 1719–1746  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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