Uniform estimates near the initial state for solutions of the two-phase parabolic problem
Algebra i analiz, Tome 25 (2013) no. 2, pp. 63-74.

Voir la notice de l'article provenant de la source Math-Net.Ru

Optimal regularity near the initial state is established for weak solutions of the two-phase parabolic obstacle problem. The approach is sufficiently general to allow the initial data to belong to the class C1,1.
Mots-clés : two-phase parabolic obstacle problem, free boundary, optimal regularity.
@article{AA_2013_25_2_a2,
     author = {D. E. Apushkinskaya and N. N. Uraltseva},
     title = {Uniform estimates near the initial state for solutions of the two-phase parabolic problem},
     journal = {Algebra i analiz},
     pages = {63--74},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2013},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/AA_2013_25_2_a2/}
}
TY  - JOUR
AU  - D. E. Apushkinskaya
AU  - N. N. Uraltseva
TI  - Uniform estimates near the initial state for solutions of the two-phase parabolic problem
JO  - Algebra i analiz
PY  - 2013
SP  - 63
EP  - 74
VL  - 25
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/AA_2013_25_2_a2/
LA  - en
ID  - AA_2013_25_2_a2
ER  - 
%0 Journal Article
%A D. E. Apushkinskaya
%A N. N. Uraltseva
%T Uniform estimates near the initial state for solutions of the two-phase parabolic problem
%J Algebra i analiz
%D 2013
%P 63-74
%V 25
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/AA_2013_25_2_a2/
%G en
%F AA_2013_25_2_a2
D. E. Apushkinskaya; N. N. Uraltseva. Uniform estimates near the initial state for solutions of the two-phase parabolic problem. Algebra i analiz, Tome 25 (2013) no. 2, pp. 63-74. https://geodesic-test.mathdoc.fr/item/AA_2013_25_2_a2/

[1] Apushkinskaya D. E., Uraltseva N. N., “Boundary estimates for solutions to the two-phase parabolic obstacle problem”, J. Math. Sci. (N.Y.), 156:4 (2009), 569–576 ; Probl. mat. analiza, 38, 2008, 3–10 | DOI | MR | Zbl

[2] Caffarelli L. A., Kenig C. E., “Gradient estimates for variable coefficient parabolic equations and singular perturbation problems”, Amer. J. Math., 120:2 (1998), 391–439 | DOI | MR | Zbl

[3] Caffarelli L., Salsa S., A geometric approach to free boundary problems, Grad. Stud. in Math., 68, Amer. Math. Soc., Providence, RI, 2005 | MR | Zbl

[4] Gilbarg D., Trudinger N. S., Elliptic partial differential equations of second order, Classics in Mathematics, Reprint of the 1998 edition, Springer-Verlag, Berlin, 2001, xiv+517 pp. | MR | Zbl

[5] Ladyženskaja O. A., Solonnikov V. A., Ural'ceva N. N., Linear and quasilinear equations of parabolic type, Transl. Math. Monogr., 23, Amer. Math. Soc., Providence, RI, 1967, xi+648 pp. | MR

[6] Ladyzhenskaya O. A., Uraltseva N. N., Linear and quasilinear elliptic equations, Acad. Press, New York, 1968, xviii+495 pp. | MR | Zbl

[7] Nyström K., Pascucci A., Polidoro S., “Regularity near the initial state in the obstacle problem for a class of hypoelliptic ultraparabolic operators”, J. Differential Equations, 249:8 (2010), 2044–2060 | DOI | MR

[8] Nazarov A. I., Uraltseva N. N., “Neravenstvo Garnaka i svyazannye s nim svoistva reshenii ellipticheskikh i parabolicheskikh uravnenii s bezdivergentnymi mladshimi koeffitsientami”, Algebra i analiz, 23:1 (2011), 136–168 | MR

[9] Nyström K., “On the behaviour near expiry for multi-dimensional American options”, J. Math. Anal. Appl., 339:1 (2008), 644–654 | DOI | MR

[10] Shahgholian H., “Free boundary regularity close to initial state for parabolic obstacle problem”, Trans. Amer. Math. Soc., 360:4 (2008), 2077–2087 | DOI | MR | Zbl

[11] Shahgholian H., Uraltseva N., Weiss G. S., “A parabolic two-phase obstacle-like equation”, Adv. Math., 221:3 (2009), 861–881 | DOI | MR | Zbl

[12] Uraltseva N. N., “Boundary estimates for solutions of elliptic and parabolic equations with discontinuous nonlinearities”, Nonlinear equations and spectral theory, Amer. Math. Soc. Transl. Ser. 2, 220, Amer. Math. Soc., Providence, RI, 2007, 235–246 | MR | Zbl