WIAS Preprint No. 1571, (2010)

Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface


Authors

  • Druet, Pierre-Étienne
    ORCID: 0000-0001-5303-0500

2010 Mathematics Subject Classification

  • 35B65 35J25

Keywords

  • Elliptic transmission problems, regularity theory, Lipschitz continuity

DOI

10.20347/WIAS.PREPRINT.1571

Abstract

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.

Appeared in

  • Math. Bohem., 138 (2013) pp. 185--224.

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