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Elliptic model problems including mixed boundary conditions and material heterogeneities. (English) Zbl 1132.35022

Elliptic problems with mixed boundary conditions in the case of heterogeneous media are considered. It is shown that \(-\nabla \cdot \mu \nabla \) is a topological isomorphism Sobolev space onto dual space for a bounded Lipschitz domain. The connection between the regularity of the solution and edge singularities is established.

MSC:

35B65 Smoothness and regularity of solutions to PDEs
35J25 Boundary value problems for second-order elliptic equations
35R05 PDEs with low regular coefficients and/or low regular data
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