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.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 48, No. 3, pp. 63–83, 2014
Original Russian Text Copyright © by R. Haller-Dintelmann, W. Höppner, H.-C. Kaiser, J. Rehberg, and G. M. Ziegler
Research by GMZ is supported by DFG Research Center Matheon and by ERC Advanced Grant agreement no. 247029-SDModels.
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Haller-Dintelmann, R., Höppner, W., Kaiser, H.C. et al. Optimal elliptic Sobolev regularity near three-dimensional multi-material Neumann vertices. Funct Anal Its Appl 48, 208–222 (2014). https://doi.org/10.1007/s10688-014-0062-z
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DOI: https://doi.org/10.1007/s10688-014-0062-z