Hölder gradient estimates on Lp-viscosity solutions of fullynonlinear parabolic equations with VMO coefficients

被引:0
作者
Tateyama, Shota [1 ]
机构
[1] Univ Tokyo, Grad Sch Math Sci, 3-8-1 Komaba,Meguro Ku, Tokyo 1538914, Japan
来源
PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2021年 / 2卷 / 06期
关键词
Fully nonlinear parabolic equations; Regularity of solutions; Viscosity solutions; Vanishing mean oscillation; REGULARITY THEORY;
D O I
10.1007/s42985-021-00133-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The local H & ouml;lder continuity estimate on the space derivative of L-p-viscosity solutions of fullynonlinear uniformly second-order parabolic partial differential equations with coefficients in vanishing mean oscillation in the space variables is established when p > n+2.
引用
收藏
页数:22
相关论文
共 23 条
[1]   Holder regularity for the gradient of the inhomogeneous parabolic normalized p-Laplacian [J].
Attouchi, Amal ;
Parviainen, Mikko .
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2018, 20 (04)
[2]   A new stability result for viscosity solutions of nonlinear parabolic equations with weak convergence in time [J].
Barles, Guy .
COMPTES RENDUS MATHEMATIQUE, 2006, 343 (03) :173-178
[3]  
Caffarelli L, 1996, COMMUN PUR APPL MATH, V49, P365
[4]   INTERIOR A PRIORI ESTIMATES FOR SOLUTIONS OF FULLY NON-LINEAR EQUATIONS [J].
CAFFARELLI, LA .
ANNALS OF MATHEMATICS, 1989, 130 (01) :189-213
[5]  
CAFFARELLI LA, 1995, AM MATH SOC COLLOQ P, V43
[6]  
Crandall MG, 1998, INDIANA U MATH J, V47, P1293
[7]   LP-Theory for fully nonlinear uniformly parabolic equations. [J].
Crandall, MG ;
Kocan, M ;
Swiech, A .
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2000, 25 (11-12) :1997-2053
[8]   USERS GUIDE TO VISCOSITY SOLUTIONS OF 2ND-ORDER PARTIAL-DIFFERENTIAL EQUATIONS [J].
CRANDALL, MG ;
ISHII, H ;
LIONS, PL .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 27 (01) :1-67
[9]   W2,N A-PRIORI ESTIMATES FOR SOLUTIONS TO FULLY NONLINEAR EQUATIONS [J].
ESCAURIAZA, L .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1993, 42 (02) :413-423
[10]  
Ishii H., 1985, Bull. Fac. Sci. Engrg. Chuo Univ, V28, P33