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Estimates of the location of a free boundary for the obstacle and stefan problems obtained by means of some energy methods


Díaz Díaz, Jesús Ildefonso (2008) Estimates of the location of a free boundary for the obstacle and stefan problems obtained by means of some energy methods. Georgian Mathematical Journal, 15 (3). pp. 475-484. ISSN 1072-947X

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In this paper we use some energy methods to study the location (and formation) of a free boundary arising in some unilateral problems, for instance, in the obstacle problem and the Stefan problem.

Item Type:Article
Uncontrolled Keywords:variational-inequalities; equations; support; formation and location of the free boundary; obstacle problem; stefan problem; energy method
Subjects:Sciences > Mathematics > Differential equations
ID Code:15215

S. N. Antontsev, J. I. Díaz, and S. I. Shmarev, Energy methods for free boundary problems. Applications to nonlinear PDEs and fluid mechanics. Progress in Nonlinear Differential Equations and their Applications, 48. Birkhäuser Boston, Inc., Boston, MA, 2002.

A. Bensoussan and J.-L. Lions, On the support of the solution of some variational inequalities of evolution. J. Math. Soc. Japan 28(1976), No. 1, 1–17.

A. Bensoussan and J.-L. Lions, Applications des inéquations variationnelles en controle stochastique. Méthodes Mathématiques de l’Informatique, No. 6. Dunod, Paris, 1978.

A. Bensoussan and J.-L. Lions, Contrôle impulsionnel et inéquations quasi variationnelles. (French) [Impulse control and quasivariational inequalities] Méthodes Mathématiques de l’Informatique [Mathematical Methods of Information Science], 11. Gauthier-Villars, Paris, 1982.

H. Brézis and A. Friedman, Estimates on the support of solutions of parabolic variational inequalities. Illinois J. Math. 20(1976), No. 1, 82–97.

N. Calvo, J. I. Díaz, J. Durany, E. Schiavi, and C. Vázquez, On a doubly nonlinear parabolic obstacle problem modelling ice sheet dynamics. SIAM J. Appl. Math. 63(2002), No. 2, 683–707 (electronic).

J. I. Díaz, Mathematical analysis of some diffusive energy balance models in climatology. Mathematics, climate and environment (Madrid, 1991), 28–56, RMA Res. Notes Appl. Math., 27, Masson, Paris, 1993.

J. I. Díaz, work in preparation.

J. I. Díaz and L. Véron, Local vanishing properties of solutions of elliptic and parabolic quasilinear equations. Trans. Amer. Math. Soc. 290(1985), No. 2, 787–814.

G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique. Travaux et Recherches Math´ematiques, No. 21. Dunod, Paris, 1972.

L. C. Evans and B. Knerr, Instantaneous shrinking of the support of nonnegative

solutions to certain nonlinear parabolic equations and variational inequalities. Illinois J.

Math. 23(1979), No. 1, 153–166.

A. Friedman, Variational principles and free-boundary problems. A Wiley-Interscience Publication. Pure and Applied Mathematics. John Wiley & Sons, Inc., New York, 1982.

R. Glowinski, J.-L. Lions, and R. Tremolieres, Analyse numérique des inéquations variationnelles. Tome 2. Applications aux phénomènes stationnaires et d’évolution. Méthodes Mathématiques de l’Informatique, 5. Dunod, Paris, 1976.

J.-L. Lions, Quelques Méthodes de résolution des problèmes aux limites non linéaires. Dunod; Gauthier-Villars, Paris, 1969.

J.-L. Lions, El planeta Tierra. El papel de las Matemáticas y de los superordenadores. Serie del Instituto de España 8, Espasa-Calpe, Madrid, 1990.

J.-L. Lions and G. Stampacchia, Inéquations variationnelles non coercives. C. R. Acad.

Sci. Paris 261(1965), 25–27.

J.-L. Lions and G. Stampacchia, Variational inequalities. Comm. Pure Appl. Math. 20(1967), 493–519.

A. M. Meirmanov, The Stefan problem. (Translated from the Russian) de Gruyter Expositions in Mathematics, 3. Walter de Gruyter & Co., Berlin, 1992.

L. Nirenberg, An extended interpolation inequality. Ann. Scuola Norm. Sup. Pisa (3) 20(1966), 733–737.

L. Tartar, Personal communication, 1976.

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