Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface
- Druet, Pierre-Étienne
2010 Mathematics Subject Classification
- 35B65 35J25
- Elliptic transmission problems, regularity theory, Lipschitz continuity
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.
- Math. Bohem., 138 (2013) pp. 185--224.