On C^1+α regularity of solutions of Isaacs parabolic equations with VMO coefficients

2012/11/20 by Krylov, N. V.
#35B65 #35D40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.4882

Abstract

We prove that boundary value problems for fully nonlinear second-order parabolic equations admit L_p-viscosity solutions, which are in C^1+α for an α∈(0,1). The equations have a special structure that the "main" part containing only second-order derivatives is given by a positive homogeneous function of second-order derivatives and as a function of independent variables it is measurable in the time variable and, so to speak, VMO in spatial variables.

Related

• Uniqueness for L_p-viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms
• C^1+α-regularity of viscosity solutions of general nonlinear parabolic equations
• To the theory of viscosity solutions for uniformly parabolic Isaacs equations
• Twice differentiability of solutions to fully nonlinear parabolic equations near the boundary
• Sharp regularity estimates for second order fully nonlinear parabolic\n equations