A Harnack Inequality Approach to the Regularity of Free Boundaries. Part I: Lipschitz Free Boundaries are C1,a.

• Autores: Luis A. Caffarelli
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 3, Nº 2, 1987, págs. 139-162
• Idioma: inglés
• DOI: 10.4171/rmi/47
• Títulos paralelos:
  • Una aproximación basada en la desigualdad de Harnack a la regularidad de las fronteras libres. Parte I: Las fronteras libres de Lipschitz son C1,a.
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• Resumen

  • 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 properties), (c) showing that near a flat point free-boundaries are Lipschitz graphs, and (d) showing that Lipschitz free boundaries are really C1,a.