# A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C1,α.

Revista Matemática Iberoamericana (1987)

- Volume: 3, Issue: 2, page 139-162
- ISSN: 0213-2230

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topCaffarelli, Luis A.. "A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C1,α.." Revista Matemática Iberoamericana 3.2 (1987): 139-162. <http://eudml.org/doc/39343>.

@article{Caffarelli1987,

abstract = {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,α.},

author = {Caffarelli, Luis A.},

journal = {Revista Matemática Iberoamericana},

keywords = {Problemas de frontera libre; Función armónica; Soluciones; existence; two-phase free-boundary problem; Lipschitz free boundaries; regularity},

language = {eng},

number = {2},

pages = {139-162},

title = {A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C1,α.},

url = {http://eudml.org/doc/39343},

volume = {3},

year = {1987},

}

TY - JOUR

AU - Caffarelli, Luis A.

TI - A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C1,α.

JO - Revista Matemática Iberoamericana

PY - 1987

VL - 3

IS - 2

SP - 139

EP - 162

AB - 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,α.

LA - eng

KW - Problemas de frontera libre; Función armónica; Soluciones; existence; two-phase free-boundary problem; Lipschitz free boundaries; regularity

UR - http://eudml.org/doc/39343

ER -

## Citations in EuDML Documents

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- L. Fornari, Regularity of the free boundary for non degenerate phase transition problems of parabolic type
- Luis A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on $X$
- Claudia Lederman, Noemi Wolanski, Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem
- Eduardo V. Teixeira, A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary
- Avner Friedman, Yong Liu, A free boundary problem arising in magnetohydrodynamic system
- John L. Lewis, Kaj Nyström, Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains

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