A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on
Luis A. Caffarelli (1988)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Luis A. Caffarelli (1988)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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...
Erik Lindgren, Henrik Shahgholian, Anders Edquist (2009)
Annales de l'I.H.P. Analyse non linéaire
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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,...
John L. Lewis, Kaj Nyström (2007)
Annales scientifiques de l'École Normale Supérieure
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L. Fornari (2000)
Rendiconti del Seminario Matematico della Università di Padova
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