Optimal Elliptic Sobolev Regularity Near Three-Dimensional Multi-Material Neumann Vertices

R. Haller-Dintelmann ; W. Höppner ; H.-Ch. Kaiser ; J. Rehberg ; G. M. Ziegler

Funkcionalʹnyj analiz i ego priloženiâ, Tome 48 (2014) no. 3, pp. 63-83.

Résumé

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 $p>3$.

Détail

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.

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