On the continuity of the time derivative of the solution to the parabolic obstacle problem with variable coefficients

Journal des Mathematiques Pures et Appliquees

Volumn 85, Issue 3, 2006, Pages 371-414

  Blanchet, Adrien ^a,b   Dolbeault, Jean ^a   Monneau, Régis ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b UNIVERSITÉ PARIS EST   (France)

Author keywords

Blow up; Free boundary; Liouville's result; Monotonicity formula; Parabolic obstacle problem

Indexed keywords

EID: 33644592006     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matpur.2005.08.007     Document Type: Article

References (30)

1. Y. Achdou An inverse problem for a parabolic variational inequality arising in volatility calibration with American options SIAM J. Control Optim. 43 5 2005 1583-1615 (electronic)
2. H.W. Alt D. Phillips A free boundary problem for semilinear elliptic equations J. Reine Angew. Math. 368 1986 63-107
3. A. Bensoussan J.-L. Lions Applications des inéquations variationnelles en contrôle stochastique Méthodes Mathématiques de l'Informatique vol. 6 1978 Dunod Paris
4. T. Björk Interest rate theory Financial Mathematics (Bressanone, 1996) Lecture Notes in Math. vol. 1656 1997 Springer-Verlag Berlin 53-122
5. F. Black M. Scholes The pricing of options and corporate liabilities J. Polit. Econ. 81 1973 637-659
6. H. Brezis Analyse fonctionnelle: Théorie et applications Theory and applications Collection Mathématiques Appliquées pour la Maîtrise Collection of Applied Mathematics for the Master's Degree 1983 Masson Paris
7. L. Caffarelli A. Petrosyan H. Shahgholian Regularity of a free boundary in parabolic potential theory J. Amer. Math. Soc. 17 2004 827-869 (electronic)
8. L.A. Caffarelli The regularity of free boundaries in higher dimensions Acta Math. 139 1977 155-184
9. C. Ciliberto Formule di maggiorazione e teoremi di esistenza per le soluzioni delle equazioni paraboliche in due variabili Ricerche Mat. 3 1954 40-75
10. P. Dupuis H. Wang Optimal stopping with random intervention times Adv. Appl. Probab. 34 2002 141-157
11. H. Federer Geometric Measure Theory Die Grundlehren Math. Wiss. vol. 153 1969 Springer-Verlag New York Inc. New York
12. A. Friedman Partial Differential Equations of Parabolic Type 1964 Prentice-Hall Inc. Englewood Cliffs, NJ
13. A. Friedman Parabolic variational inequalities in one space dimension and smoothness of the free boundary J. Funct. Anal. 18 1975 151-176
14. A. Friedman Variational Principles and Free-Boundary Problems second ed. 1988 Robert E. Krieger Publishing Co. Inc. Malabar, FL
15. Y. Giga R.V. Kohn Asymptotically self-similar blow-up of semilinear heat equations Comm. Pure Appl. Math. 38 1985 297-319
16. P. Jaillet D. Lamberton B. Lapeyre Variational inequalities and the pricing of American options Acta Appl. Math. 21 1990 263-289
17. D. Kinderlehrer G. Stampacchia An Introduction to Variational Inequalities and Their Applications Pure Appl. Math. vol. 88 1980 Academic Press Inc. (Harcourt Brace Jovanovich Publishers) New York
18. O.A. Ladyženskaja V.A. Solonnikov N.N. Ural'ceva Linear and Quasilinear Equations of Parabolic Type Transl. Math. Monogr. vol. 23 1967 Amer. Math. Soc. Providence, RI Translated from the Russian by S. Smith
19. D. Lamberton B. Lapeyre Introduction au calcul stochastique appliqué à la finance second ed. 1997 Ellipses Édition Marketing Paris
20. G.M. Lieberman Second Order Parabolic Differential Equations 1996 World Scientific Publishing Co. Inc. River Edge, NJ
21. R. Monneau On the number of singularities for the obstacle problem in two dimensions J. Geom. Anal. 13 2003 359-389
22. B. Øksendal Stochastic Differential Equations Universitext 1985 Springer-Verlag Berlin An introduction with applications
23. H. Pham Optimal stopping of controlled jump diffusion processes: A viscosity solution approach J. Math. Systems Estim. Control 8 1998 27 (electronic)
24. G. Rapuch American options and the free boundary exercise region: A PDE approach Interfaces Free Bound. 7 1 2005 79-98
25. J.-F. Rodrigues Obstacle Problems in Mathematical Physics North-Holland Mathematics Studies vol. 134 1987 North-Holland Publishing Co. Amsterdam Notas de Matemática (Mathematical Notes), 114
26. P. Van Moerbeke An optimal stopping problem with linear reward Acta Math. 132 1974 111-151
27. S. Villeneuve, Options américaines dans un modèle de Black-Scholes multidimensionnel, PhD thesis, Université de Marne-la-Vallée, 1999
28. G.S. Weiss Self-similar blow-up and Hausdorff dimension estimates for a class of parabolic free boundary problems SIAM J. Math. Anal. 30 1999 623-644 (electronic)
29. G.S. Weiss The free boundary of a thermal wave in a strongly absorbing medium J. Differential Equations 160 2000 357-388
30. D.V. Widder The Heat Equation Pure Appl. Math. vol. 67 1975 Academic Press (Harcourt Brace Jovanovich Publishers) New York