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Abstract:

In this manuscript we establish Schauder type estimates for viscosity solutions with small enough oscillation to non-convex fully nonlinear second order parabolic equations of the following form ∂u∂t−F(x,t,D2u)=f(x,t)inQ1=B1×(−1,0],provided that the source f and the coefficients of F are Dini continuous functions. Furthermore, for problems with merely continuous data, we prove that such solutions are parabolically C1,Log-Lip smooth. Finally, we put forward a number of applications consequential of our estimates, which include a partial regularity result and a theorem of Schauder type for classical solutions. © 2017, Springer Science+Business Media B.V., part of Springer Nature.

Registro:

Documento: Artículo
Título:Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications
Autor:da Silva, J.V.; Dos Prazeres, D.
Filiación:Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, Universidad de Buenos Aires, Buenos Aires, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria - Pabellón I (1428) Av. Cantilo s/n, Buenos Aires, Argentina
Palabras clave:Flat viscosity solutions; Fully nonlinear parabolic equations; Schauder type estimates
Año:2019
Volumen:50
Número:2
Página de inicio:149
Página de fin:170
DOI: http://dx.doi.org/10.1007/s11118-017-9677-z
Título revista:Potential Analysis
Título revista abreviado:Potential Anal.
ISSN:09262601
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09262601_v50_n2_p149_daSilva

Referencias:

  • Armstrong, S., Silvestre, L., Smart, C., Partial regularity of solutions of fully nonlinear, uniformly elliptic equations (2012) Comm. Pure Appl. Math, 65, pp. 1169-1184
  • Caffarelli, L.A., Stefanelli, U., A counterexample to C2,1 regularity for parabolic fully nonlinear equations (2008) Comm. Partial Differential Equations, 33 (7-9), pp. 1216-1234
  • Chen, Y.Z., Zou, X., Fully nonlinear parabolic equations and the dini condition (2002) Acta Math. Sin-English Series, 18 (3), pp. 473-480
  • Crandall, M.G., Kocan, M., Swiech, A., Lp-theory for fully nonlinear uniformly parabolic equations (2000) Comm. Partial Differential Equations, 25 (11-12), pp. 1997-2053
  • Daniel, J.-P., Quadratic expansions and partial regularity for fully nonlinear uniformly parabolic equations (2015) Calc. Var. Partial Differential Equations, 54, pp. 183-216
  • da Silva, J.V., Teixeira, E.V., Sharp regularity estimates for second order fully nonlinear parabolic equations (2017) Math. Ann., 369 (3-4), pp. 1623-1648
  • Huisken, G., The volume preserving mean curvature flow (1987) J. für die Reine und Angewandte Mathematik, 382, pp. 35-48
  • Il’in, A.M., On parabolic equations whose coefficients do not satisfy the Dini condition (1967) Mat. Zametki, 1 (1), pp. 71-80
  • Kovats, J., Dini-Campanato spaces and applications to nonlinear elliptic equations (1999) Electron. J. Diff. Equa., 1999 (37), pp. 1-20
  • Kruzhkov, S.N., Estimates for the highest derivatives of solutions of elliptic and parabolic equations with continuous coefficients (1967) Mat. Zametki, 2 (5), pp. 549-560
  • Krylov, N., Boundedly inhomogeneous elliptic and parabolic equations in a domain (1983) Izv. Akad. Nak. SSSR. Ser. Mat., 47, pp. 75-108. , English transl. Math USSR Izv., 22, 1, 67–97, 1984
  • Krylov, N., (1996) Lectures on Elliptic and Parabolic Equations in Hölder Spaces. Graduate Studies in Mathematics, vol. 12, , American Mathematical Society, Providence: xii+ 164
  • Krylov, N., Safonov, M., A certain properties of solutions of parabolic equations with measurable coefficients (1981) Math. USSR Izv., 16 (1), pp. 151-164
  • Lieberman, G.M., (1996) Second Order Parabolic Differential Equations, , World Scientific Publishing Co Inc., River Edge
  • Nadirashvili, N., Vlăduţ, S., Nonclassical solutions of fully nonlinear elliptic equations (2007) Geom. Funct Anal., 17 (4), pp. 1283-1296
  • Nadirashvili, N., Vlăduţ, S., Singular viscosity solutions to fully nonlinear elliptic equations (2008) J. Math Pure Appl. (9), 89 (2), pp. 107-113
  • Nadirashvili, N., Vlăduţ, S., Nonclassical solutions of fully nonlinear elliptic equations II. Hessian equations and octonions (2011) Geom. Funct. Anal., 21, pp. 483-498
  • Nadirashvili, N., Vlăduţ, S., Octonions and singular solutions of Hessian elliptic equations (2011) Geom. Funct. Anal., 21 (2), pp. 483-498
  • Nadirashvili, N., Vlăduţ, S., Singular solutions of Hessian elliptic equations in five dimensions (2013) J. Math. Pures Appl., 100, pp. 769-784
  • Prazeres, D., Teixeira, E.V., Asymptotics and regularity of flat solutions to fully nonlinear elliptic problems (2016) Ann. Sc. Norm. Super. Pisa Cl. Sci., 15, pp. 485-500
  • Savin, O., Small perturbation solutions for elliptic equations (2007) Comm. Partial Differential Equations, 32 (4-6), pp. 557-578
  • Sheng, W., Wang, X.-J., Regularity and singularity in mean curvature flow. Trends in Partial Differential Equations (2010) Adv. Lect. Math, pp. 399-436
  • Teixeira, E.V., Universal moduli of continuity for solutions to fully nonlinear elliptic equations (2014) Arch. Rational Mech. Anal., 211 (3), pp. 911-927
  • Teixeira, E.V., Geometric regularity estimates for elliptic equations (2013) Proc. MCA Contemp. Math., 656 (2016), pp. 185-204
  • 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
  • Tian, G., Wang, X.-J., A priori estimates for fully nonlinear parabolic equations (2012) Int. Math. Res Notices, 2012, pp. 1-21
  • Wang, L., On the regularity theory of fully nonlinear parabolic equations: I (1992) Comm. Pure Appl. Math., 45, pp. 27-76
  • Wang, L., On the regularity theory of fully nonlinear parabolic equations: II (1992) Comm. Pure Appl. Math., 45, pp. 141-178
  • Wang, Y., Small perturbation solutions for parabolic equations (2013) Indiana Univ. Math. J., 62 (2), pp. 671-698

Citas:

---------- APA ----------
da Silva, J.V. & Dos Prazeres, D. (2019) . Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications. Potential Analysis, 50(2), 149-170.
http://dx.doi.org/10.1007/s11118-017-9677-z
---------- CHICAGO ----------
da Silva, J.V., Dos Prazeres, D. "Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications" . Potential Analysis 50, no. 2 (2019) : 149-170.
http://dx.doi.org/10.1007/s11118-017-9677-z
---------- MLA ----------
da Silva, J.V., Dos Prazeres, D. "Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications" . Potential Analysis, vol. 50, no. 2, 2019, pp. 149-170.
http://dx.doi.org/10.1007/s11118-017-9677-z
---------- VANCOUVER ----------
da Silva, J.V., Dos Prazeres, D. Schauder Type Estimates for “Flat” Viscosity Solutions to Non-convex Fully Nonlinear Parabolic Equations and Applications. Potential Anal. 2019;50(2):149-170.
http://dx.doi.org/10.1007/s11118-017-9677-z