Navegar

Colección

Datos Estadísticas

Artículo

Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We prove sharp regularity estimates for viscosity solutions of fully nonlinear parabolic equations of the form (Formula Presented.)where F is elliptic with respect to the Hessian argument and f∈ Lp , q(Q1). The quantity Ξ(n,p,q):=np+2q determines to which regularity regime a solution of (Eq) belongs. We prove that when 1 < Ξ (n, p, q) < 2 - ϵF, solutions are parabolically α-Hölder continuous for a sharp, quantitative exponent 0 < α(n, p, q) < 1. Precisely at the critical borderline case, Ξ (n, p, q) = 1 , we obtain sharp parabolic Log-Lipschitz regularity estimates. When 0 < Ξ (n, p, q) < 1 , solutions are locally of class C1+σ,1+σ2 and in the limiting case Ξ (n, p, q) = 0 , we show parabolic C1 , Log-Lip regularity estimates provided F has “better” a priori estimates. © 2016, Springer-Verlag Berlin Heidelberg.

Registro:

Documento: Artículo
Título:Sharp regularity estimates for second order fully nonlinear parabolic equations
Autor:da Silva, J.V.; Teixeira, E.V.
Filiación:Department of Mathematics, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria-Pabellón I-(C1428EGA), Buenos Aires, Argentina
Departmento de Matemática, Universidade Federal do Ceará, Campus do Pici, Bloco 914, Fortaleza, CE CEP: 60455-760, Brazil
Palabras clave:35B65; 35K10
Año:2017
Volumen:369
Número:3-4
Página de inicio:1623
Página de fin:1648
DOI: http://dx.doi.org/10.1007/s00208-016-1506-y
Título revista:Mathematische Annalen
Título revista abreviado:Math. Ann.
ISSN:00255831
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255831_v369_n3-4_p1623_daSilva

Referencias:

  • Caffarelli, L.A., Stefanelli, U., A counterexample to C2, 1 regularity for parabolic fully nonlinear equations (2008) Commun. Partial Differ. Equ., 33 (7-9), pp. 1216-1234
  • Crandall, M.G., Fok, P.-K., Kocan, M., Swiech, A., Remarks on nonlinear uniformly parabolic equations (1998) Indiana Univ. Math. J., 47 (4), pp. 1293-1326
  • Crandall, M.G., Kocan, M., Lions, P.-L., Swiech, A., Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations (1999) Electron. J. Differ. Equ., 1999 (24), pp. 1-20
  • Crandall, M.G., Kocan, M., Swiech, A., Lp -theory for fully nonlinear uniformly parabolic equations (2000) Commun. Partial Differ. Equ., 25 (11-12), pp. 1997-2053
  • Crandall, M.G., Swiech, A., (2003) A note on generalized maximum principles for elliptic and parabolic PDE. Evolution equations, 121-127, Lecture Notes in Pure and Appl. Math., vol., , Dekker, New York
  • Escauriaza, L., W2 , n a priori estimates for solutions to fully non-linear elliptic equations (1993) Indiana Univ. Math. J., 42 (2), pp. 413-423
  • Evans, L.C., Classical solutions of fully nonlinear, convex, second-order elliptic equations (1982) Commun. Pure Appl. Math., 35 (3), pp. 333-363
  • Imbert, C., Silvestre, L., An introduction to fully nonlinear parabolic equations (2013) Boucksom, S., Eyssidieux, P., Guedj, V. (eds) An Introduction to the Kähler-Ricci Flow. Lecture Notes in Mathematics, vol. 2086, pp. 7–88. Springer
  • Kim, D., Elliptic and parabolic equations with measurable coefficients in Lp -spaces with mixed norms (2008) Methods Appl. Anal., 15 (4), pp. 437-468
  • Kim, D., Parabolic equations with partially BMO coefficients and boundary value problems in Sobolev spaces with mixed norms (2010) Potential Anal., 33, pp. 17-46
  • N.V.: Boundedly nonhomogeneous elliptic and parabolic equations. Izv. Akad. Nak. SSSR. Ser. Mat. 46 (1982) In Math USSR Izv, , Krylov[English transl.20, 459–492 (1983)]
  • N.V.: Boundedly nonhomogeneous elliptic and parabolic equations in a domain (1983) Izv. Akad. Nak. SSSR. Ser. Mat, , Krylov[English transl. in Math USSR Izv. 22, 67–97 (1984)]
  • Krylov, N.V., (2008) Lectures on elliptic and parabolic equations in Sobolev spaces. Graduate Studies in Mathematics, , American Mathematical Society, USA
  • Krylov, N.V., Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms (2007) J. Funct. Anal., 250, pp. 521-558
  • M.V.: An estimate of the probability that a diffusion process hits a set of positive measure (1979) Dokl. Akad. Nauk. SSSR, , Krylov, N.V., Safonov[English translation in Soviet Math Dokl. 20, 235–255 (1979)]
  • Krylov, N.V., Safonov, M.V., Certain properties of solutions of parabolic equations with measurable coefficients (1980) Izvestia Akad Nauk. SSSR, 40, pp. 161-175
  • Sheng, W., Wang, X.-J., Regularity and singularity in mean curvature flow. Trends in Partial Differential Equations. Adv. Lect (2010) Math., pp. 399-436
  • Teixeira, E.V., Universal moduli of continuity for solutions to fully nonlinear elliptic equations (2014) Arch. Ration. Mech. Anal., 211 (3), pp. 911-927
  • Teixeira, E.V., Urbano, J.M., A geometric tangential approach to sharp regularity for degenerate evolution equations (2014) Anal. PDE, 7 (3), pp. 733-744
  • Wang, L., On the regularity theory of fully nonlinear parabolic equations: I (1992) Commun. Pure Appl. Math., 45, pp. 27-76
  • Wang, L., On the regularity theory of fully nonlinear parabolic equations: II (1992) Commun. Pure Appl. Math., 45, pp. 141-178

Citas:

---------- APA ----------
da Silva, J.V. & Teixeira, E.V. (2017) . Sharp regularity estimates for second order fully nonlinear parabolic equations. Mathematische Annalen, 369(3-4), 1623-1648.
http://dx.doi.org/10.1007/s00208-016-1506-y
---------- CHICAGO ----------
da Silva, J.V., Teixeira, E.V. "Sharp regularity estimates for second order fully nonlinear parabolic equations" . Mathematische Annalen 369, no. 3-4 (2017) : 1623-1648.
http://dx.doi.org/10.1007/s00208-016-1506-y
---------- MLA ----------
da Silva, J.V., Teixeira, E.V. "Sharp regularity estimates for second order fully nonlinear parabolic equations" . Mathematische Annalen, vol. 369, no. 3-4, 2017, pp. 1623-1648.
http://dx.doi.org/10.1007/s00208-016-1506-y
---------- VANCOUVER ----------
da Silva, J.V., Teixeira, E.V. Sharp regularity estimates for second order fully nonlinear parabolic equations. Math. Ann. 2017;369(3-4):1623-1648.
http://dx.doi.org/10.1007/s00208-016-1506-y