Free boundary regularity in Stefan type problems

Ioannis Athanasopoulos

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2004)

  • Volume: 15, Issue: 3-4, page 345-355
  • ISSN: 1120-6330

Abstract

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Regularity results of free boundaries for Stefan type problems are discussed. The influence that curvature may have on the behavior of the free boundary is studied and various open problems are also mentioned.

How to cite

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Athanasopoulos, Ioannis. "Free boundary regularity in Stefan type problems." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.3-4 (2004): 345-355. <http://eudml.org/doc/252281>.

@article{Athanasopoulos2004,
abstract = {Regularity results of free boundaries for Stefan type problems are discussed. The influence that curvature may have on the behavior of the free boundary is studied and various open problems are also mentioned.},
author = {Athanasopoulos, Ioannis},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Free boundary problem; Stefan problem; Regularity; Curvature; Viscosity solution},
language = {eng},
month = {12},
number = {3-4},
pages = {345-355},
publisher = {Accademia Nazionale dei Lincei},
title = {Free boundary regularity in Stefan type problems},
url = {http://eudml.org/doc/252281},
volume = {15},
year = {2004},
}

TY - JOUR
AU - Athanasopoulos, Ioannis
TI - Free boundary regularity in Stefan type problems
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/12//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 3-4
SP - 345
EP - 355
AB - Regularity results of free boundaries for Stefan type problems are discussed. The influence that curvature may have on the behavior of the free boundary is studied and various open problems are also mentioned.
LA - eng
KW - Free boundary problem; Stefan problem; Regularity; Curvature; Viscosity solution
UR - http://eudml.org/doc/252281
ER -

References

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  1. ALT, H.W. - CAFFARELLI, L.A. - FRIEDMAN, A., Variational problems with two-phases and their free boundaries. Trans. Amer. Math. Soc., 282, 1984, 431-461. Zbl0844.35137MR732100DOI10.2307/1999245
  2. ATHANASOPOULOS, I. - CAFFARELLI, L.A. - SALSA, S., Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems. Annals Math., 143, 1996, 413-434. Zbl0853.35049MR1394964DOI10.2307/2118531
  3. ATHANASOPOULOS, I. - CAFFARELLI, L.A. - SALSA, S., Regularity of the free boundary in parabolic phase transition problems. Acta Math., 176, 1996, 245-282. Zbl0891.35164MR1397563DOI10.1007/BF02551583
  4. ATHANASOPOULOS, I. - CAFFARELLI, L.A. - SALSA, S., Phase transition problems of parabolic type: flat free boundaries are smooth. Comm. Pure Appl. Math., 51, 1998, 77-112. Zbl0924.35197MR1486632DOI10.1002/(SICI)1097-0312(199801)51:1<77::AID-CPA4>3.3.CO;2-K
  5. ATHANASOPOULOS, I. - CAFFARELLI, L.A. - SALSA, S., Stefan-like problems with curvature. J. Geom. Anal., 13, 2003, 21-27. Zbl1055.35146MR1967033DOI10.1007/BF02930993
  6. CAFFARELLI, L.A. - EVANS, L.C., Continuity of the temperature in two-phase Stefan problems. Arch. Rational Mech., 81, 1983, 199-220. Zbl0516.35080MR683353DOI10.1007/BF00250800
  7. CAFFARELLI, L.A. - WANG, L., A Harnock inequality approach to the interior regularity of elliptic equations. Ind. Univ. Math. J., 42, 1993, 145-157. Zbl0810.35023MR1218709DOI10.1512/iumj.1993.42.42007
  8. FRIEDMAN, A., Variational Problems and Free Boundary Problems. Wiley, New York1982. MR679313
  9. RUBINSTEIN, L.I., Passive transfer of low-molecular nonelectrolytes across deformable membranes. I. Equations of convective-diffusion transfer of nonelectrolytes across deformable membranes of large curvature. Bull. of Math. Biology, 36, 1974, 365-377. Zbl0285.92004
  10. WANG, L., On the regularity theory of fully nonlinear parabolic equation II. Comm. Pure Appl. Math., 45, 1992, 141-178. Zbl0774.35042MR1139064DOI10.1002/cpa.3160450202
  11. WIDMAN, K.-O., Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations. Math. Scad., 21, 1967, 17-37. Zbl0164.13101MR239264

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