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:

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

Full text available as PDF.

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at

[Previous Article] [Contents of This Number] [Contents of Mathematica Bohemica]
[Full text of the older issues of Mathematica Bohemica at DML-CZ]