MATHEMATICA BOHEMICA, Vol. 138, No. 2, pp. 185-224, 2013

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

Pierre-Etienne Druet

Pierre-Etienne Druet, Weierstrass Institute for Applied Analysis and Stochastics, D-10117 Berlin, Mohrenstr. 39, Germany, e-mail: druet@wias-berlin.de

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 pair of compatibility conditions for the angle of the two surfaces and the boundary data at the contact line, we prove the existence of up to the boundary square-integrable second derivatives, and the global Lipschitz continuity of the solution. If only the weakest, necessary condition is satisfied, we show that the second weak derivatives remain integrable to a certain power less than two.

Keywords: elliptic transmission problem, regularity theory, Lipschitz continuity

Classification (MSC 2010): 35B65, 35J25

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