A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on X

Luis A. Caffarelli

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1988)

  • Volume: 15, Issue: 4, page 583-602
  • ISSN: 0391-173X

How to cite

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Caffarelli, Luis A.. "A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on $X$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 15.4 (1988): 583-602. <http://eudml.org/doc/84044>.

@article{Caffarelli1988,
author = {Caffarelli, Luis A.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Harnack inequality; interface; Lipschitz continuous, weak solution},
language = {eng},
number = {4},
pages = {583-602},
publisher = {Scuola normale superiore},
title = {A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on $X$},
url = {http://eudml.org/doc/84044},
volume = {15},
year = {1988},
}

TY - JOUR
AU - Caffarelli, Luis A.
TI - A Harnack inequality approach to the regularity of free boundaries. Part III : existence theory, compactness, and dependence on $X$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1988
PB - Scuola normale superiore
VL - 15
IS - 4
SP - 583
EP - 602
LA - eng
KW - Harnack inequality; interface; Lipschitz continuous, weak solution
UR - http://eudml.org/doc/84044
ER -

References

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  1. [A-C] H.W. Alt - L.A. Caffarelli, Existence and Regularity for a minimal problem with a free boundary, J. Reine Angew. Math325 (1981), 105-144. Zbl0449.35105MR618549
  2. [A-C-F] H.W. Alt - L.A. Caffarelli - A. Friedman, Variational problems with two phases and their free boundaries, T.A.M.S. 282 No. 2 (1984), 431-461. Zbl0844.35137MR732100
  3. [C,I] L.A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries. Part I: Lipschitz free boundaries are C1,α, Revista Matematica Iberoamericana, to appear. Zbl0676.35086
  4. [C,II] L.A. Caffarelli, A Harnack inequality approach to the regularity of free boundaries. Part II: Flat free boundaries are Lipschitz, to appear. Zbl0676.35086
  5. [L-S-W] W. Littman - G. Stampacchia - H. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. di Pisa (3) 17 (1963), 43-77. Zbl0116.30302MR161019
  6. [G] E. Giusti, Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, 1984. Zbl0545.49018MR638362
  7. [G-T] J. Gilbarg - Trudinger, Elliptic P.D.E. of Second order, 2nd Ed., Springer, New York, 1983. 

Citations in EuDML Documents

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  1. Claudia Lederman, Noemi Wolanski, Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem
  2. Eduardo V. Teixeira, A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary
  3. Avner Friedman, Yong Liu, A free boundary problem arising in magnetohydrodynamic system
  4. Sandro Salsa, Viscosity Solutions of Two-Phase Free Boundary Problems for Elliptic and Parabolic Operators
  5. John L. Lewis, Kaj Nyström, Boundary behaviour for p harmonic functions in Lipschitz and starlike Lipschitz ring domains

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