Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface
Please always quote using this URN:urn:nbn:de:0296-matheon-7413
- We investigate the regularity of the weak solution to elliptic transmission problems that involve two layered anisotropic materials separated by a boundary intersecting interface. Under a compatibility condition for the angle of contact of the two surfaces and the boundary data, we prove the existence of square-integrable second derivatives, and the global Lipschitz continuity of the solution. We show that the second weak derivatives remain integrable to a certain power less than two if the compatibility condition is violated.
Author: | Pierre-Etienne Druet |
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URN: | urn:nbn:de:0296-matheon-7413 |
Referee: | Fredi Tröltzsch |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2011/03/01 |
Release Date: | 2010/12/20 |
Tag: | |
Institute: | Technische Universität Berlin |
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) | |
MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B65 Smoothness and regularity of solutions |
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J25 Boundary value problems for second-order elliptic equations | |
Preprint Number: | 753 |