7 papers
On the parabolic Adams theorem and its applications to diffusion processes
N. V. Krylov
We show how the parabolic version of the Adams theorem and its corollary can be used to estimate in the evolution family associated to a divergence form second-order parabo…
On solvability of parabolic equations with singular coefficients in odd mixed-norm Morrey-Sobolev spaces
N. V. Krylov
We prove an existence and uniqueness theorem for second-order parabolic equations in the whole space with constant zeroth-order coefficient in mixed-norm Morrey-Sobolev spaces. The…
Extending BMO functions in parabolic setting
N. V. Krylov
We prove that one can extend any function given in a cube in to become a functions in almost preserving its $…
Essentials of Real Analysis and Morrey-Sobolev spaces for second-order elliptic and parabolic PDEs with singular first-order coefficients
N. V. Krylov
In recent years we witness growing interest in using Real Analysis methods and results in the theory of nondivergence form partial differential equations (PDEs) and the goal of thi…
On parabolic equations in Sobolev spaces with lower-order coefficients from Morrey spaces
N. V. Krylov
We consider parabolic equations with operators with being almost in VMO, in a Morrey class containing and $c…
A remark on a paper of F. Chiarenza and M. Frasca
N. V. Krylov
In 1990 F. Chiarenza and M. Frasca published a paper in which they generalized a result of C. Fefferman on estimates of the integral of through the integral of $|Du|^{p}…
Estimates in for solutions of SPDEs with coefficients in Morrey classes
N. V. Krylov
For solutions of a certain class of SPDEs in divergence form we present some estimates of their -norms and the -norms of their first-order derivatives. The main novel…