Nicolai V. Krylov

activity

20052019

most citedParabolic equations with measurable coefficients

24 citations · 66 across the 29 of their papers we have counts for

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17 papers · 1 filter

math.AP2018★ 1 cited

Weighted Aleksandrov estimates: PDE and stochastic versions

N. V. Krylov

We prove several pointwise estimates for solutions of linear elliptic (parabolic) equations with measurable coefficients in smooth domains (cylinders) through the weighted $L_{d}$ …

math.AP2017★ 1 cited

Uniqueness for $L_{p}$ -viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms

N. V. Krylov

In this article we present several results concerning uniqueness of $C$ -viscosity and $L_{p}$ -viscosity solutions for fully nonlinear parabolic equations. In case of the Isaacs equ…

math.AP2016

On an energy equality in the theory of evolution equations

N. V. Krylov

We give an elementary proof of a basic "energy" equality in the theory of evolution equations in the setting, which usually starts with introducing $V \subset H = H^{*} \subset V^{*}$ .

math.AP2016★ 7 cited

Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations

N. V. Krylov, E. Priola

We show among other things how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations w…

math.AP2014

To the theory of viscosity solutions for uniformly parabolic Isaacs equations

N. V. Krylov

We show how a theorem about the solvability in $W_{\infty}^{1, 2}$ of special parabolic Isaacs equations can be used to obtain the existence and uniqueness of viscosity solutions of…

math.AP2014★ 1 cited

To the theory of viscosity solutions for uniformly elliptic Isaacs equations

N. V. Krylov

We show how a theorem about solvability in $C^{1, 1}$ of special Isaacs equations can be used to obtain existence and uniqueness of viscosity solutions of general uniformly nondegen…

math.AP2012★ 2 cited

On the existence of smooth solutions for fully nonlinear parabolic equations with measurable "coefficients" without convexity assumptions

Hongjie Dong, Nicolai V. Krylov

We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in any cylindrical smooth domain with…

math.AP2012★ 2 cited

On the existence of smooth solutions for fully nonlinear elliptic equations with measurable "coefficients" without convexity assumptions

N. V. Krylov

We show that for any uniformly elliptic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term one can find an approximating equation…

math.AP2012★ 1 cited

Rate of convergence of difference approximations for uniformly nondegenerate elliptic Bellman's equations

N. V. Krylov

We show that the rate of convergence of solutions of finite-difference approximations for uniformly elliptic Bellman's equations is of order at least $h^{2/3}$ , where $h$ is the me…

math.AP2012★ 3 cited

On the existence of $W_{p}^{2}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions

N. V. Krylov

We establish the existence and uniqueness of solutions of fully nonlinear elliptic second-order equations like $H (v, D v, D^{2} v, x) = 0$ in smooth domains without requiring $H$ to be co…

math.AP2012★ 3 cited

Some $L_{p}$ -estimates for elliptic and parabolic operators with measurable coefficients

N. V. Krylov

We consider linear elliptic and parabolic equations with measurable coefficients and prove two types of $L_{p}$ -estimates for their solutions, which were recently used in the theor…

math.AP2010★ 1 cited

Kalman-Bucy filter and SPDEs with growing lower-order coefficients in $W_{p}^{1}$ spaces without weights

N. V. Krylov

We consider divergence form uniformly parabolic SPDEs with VMO bounded leading coefficients, bounded coefficients in the stochastic part, and possibly growing lower-order coefficie…

math.AP2010

On Bellman's equations with VMO coefficients

N. V. Krylov

We present a result about solvability in $W_{p}^{2}$ , $p > d$ , in the whole space $\bR^{d}$ of Bellman's equations with VMO ``coefficients''. Parabolic equations are touched upon as…

math.AP2008

Second-order elliptic and parabolic equations with $B (R^{2}, V M O)$ coefficients

Hongjie Dong, N. V. Krylov

The solvability in Sobolev spaces $W_{p}^{1, 2}$ is proved for nondivergence form second order parabolic equations for $p > 2$ close to 2. The leading coefficients are assumed to be mea…

math.AP2008★ 1 cited

Second-order elliptic equations with variably partially VMO coefficients

N. V. Krylov

The solvability in $W^{2}_{p}(\bR^{d})$ spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal direc…

math.AP2006★ 24 cited

Parabolic equations with measurable coefficients

Doyoon Kim, N. V. Krylov

We investigate the unique solvability of second order parabolic equations in non-divergence form in $W_p^{1,2}((0,T) \times \bR^d)$, $p \geq 2$ . The leading coefficients are only me…

math.AP2005

Parabolic and elliptic equations with VMO coefficients

N. V. Krylov

An $L_{p}$ -theory of divergence and non-divergence form elliptic and parabolic equations is presented. The main coefficients are supposed to belong to the class $V M O_{x}$ , which, i…

Weighted Aleksandrov estimates: PDE and stochastic versions

Uniqueness for Lp​-viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms

On an energy equality in the theory of evolution equations

Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations

To the theory of viscosity solutions for uniformly parabolic Isaacs equations

To the theory of viscosity solutions for uniformly elliptic Isaacs equations

On the existence of smooth solutions for fully nonlinear parabolic equations with measurable "coefficients" without convexity assumptions

On the existence of smooth solutions for fully nonlinear elliptic equations with measurable "coefficients" without convexity assumptions

Rate of convergence of difference approximations for uniformly nondegenerate elliptic Bellman's equations

On the existence of Wp2​ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions

Some Lp​-estimates for elliptic and parabolic operators with measurable coefficients

Kalman-Bucy filter and SPDEs with growing lower-order coefficients in Wp1​ spaces without weights

On Bellman's equations with VMO coefficients

Second-order elliptic and parabolic equations with B(R2,VMO) coefficients

Second-order elliptic equations with variably partially VMO coefficients

Parabolic equations with measurable coefficients

Parabolic and elliptic equations with VMO coefficients

Uniqueness for $L_{p}$ -viscosity solutions for uniformly parabolic Isaacs equations with measurable lower order terms

On the existence of $W_{p}^{2}$ solutions for fully nonlinear elliptic equations under relaxed convexity assumptions

Some $L_{p}$ -estimates for elliptic and parabolic operators with measurable coefficients

Kalman-Bucy filter and SPDEs with growing lower-order coefficients in $W_{p}^{1}$ spaces without weights

Second-order elliptic and parabolic equations with $B (R^{2}, V M O)$ coefficients