On \(C^{1+\alpha}\) regularity of solutions of Isaacs parabolic equations with VMO coefficients
type: Item
instance of: scholarly article
title: On \(C^{1+\alpha}\) regularity of solutions of Isaacs parabolic equations with VMO coefficients
zbMATH Open document ID: 1304.35173
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2014-10-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1211.4882
review text: The author proves that boundary value problems for fully nonlinear second-order parabolic equations \[ v_t+H(v,Dv,D^2v,t,x)=0 \] admit \(L_p\)-viscosity solutions, which are in \(C^{1+\alpha}\) for an \(\alpha\in(0,1).\) 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 VMO in spatial variables.
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35D40
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 6358113
zbMATH Keywords: fully nonlinear equations
zbMATH Keywords: Hölder regularity of derivatives
author: N. V. Krylov
reviewed by: Lubomira Softova
MaRDI profile type: Publication
OpenAlex ID: W2112896228
arXiv ID: 1211.4882
cites work: \(C^{1,\beta}\) regularity of viscosity solutions via a continuous-dependence result
cites work: Interior a priori estimates for solutions of fully nonlinear equations
cites work: On solving certain nonlinear partial differential equations by accretive operator methods
cites work: Lp- Theory for fully nonlinear uniformly parabolic equations
cites work: On fully nonlinear elliptic and parabolic equations with VMO coefficients in domains
cites work: A representation formula and regularizing properties for viscosity solutions of second-order fully nonlinear degenerate parabolic equations
cites work: Q5587351
cites work: ON THE MAXIMUM PRINCIPLE FOR NONLINEAR PARABOLIC AND ELLIPTIC EQUATIONS
cites work: Q3712656
cites work: On a representation of fully nonlinear elliptic operators in terms of pure second order derivatives and its applications
cites work: An Ersatz Existence Theorem for Fully Nonlinear Parabolic Equations without Convexity Assumptions
cites work: Q3726569
cites work: ON THE CLASSICAL SOLUTION OF NONLINEAR ELLIPTIC EQUATIONS OF SECOND ORDER
cites work: \(W^{1,p}\)-interior estimates for solutions of fully nonlinear, uniformly elliptic equations
cites work: Hölder gradient estimates for fully nonlinear elliptic equations
cites work: Q3475669
cites work: On the regularity theory of fully nonlinear parabolic equations: II
DOI: 10.1007/S00030-013-0238-X
description: scientific article; zbMATH DE number 6358113