4 papers
Universal estimates for parabolic equations and applications for non-linear and non-local problems
Nikolai Dokuchaev
We obtain some "universal" estimates for -norm of the solution of a parabolic equation via a weighted version of -norm of the free term. More precisely, we found the l…
Cordes conditions and some alternatives for parabolic equations and discontinuous diffusion
Nikolai Dokuchaev
The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in…
On -distance between first exit times from two regions
Nikolai Dokuchaev
First exit times from regions and their dependence on variations of boundaries are discussed for diffusion processes. The paper presents an estimate of -distance between exit…
A new property of absorbed diffusions
Nikolai Dokuchaev
We consider stochastic diffusion processes absorbed at the boundary of a domain. It is shown that there exist initial distributions which ensure a given decreasing of density of th…