Displaying similar documents to “Subsolutions of elliptic operators in divergence form and application to two-phase free boundary problems.”

A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C.

Luis A. Caffarelli (1987)

Revista Matemática Iberoamericana

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This is the first in a series of papers where we intend to show, in several steps, the existence of classical (or as classical as possible) solutions to a general two-phase free-boundary system. We plan to do so by: (a) constructing rather weak generalized solutions of the free-boundary problems, (b) showing that the free boundary of such solutions have nice measure theoretical properties (i.e., finite (n-1)-dimensional Hausdorff measure and the associated differentiability...

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

Pierre-Etienne Druet (2013)

Mathematica Bohemica

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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,...