Zobrazeno 1 - 10
of 169
pro vyhledávání: '"Semenov, Yu. P."'
Autor:
Kinzebulatov, D., Semenov, Yu. A.
We consider diffusion operator $-\Delta + b \cdot \nabla$ in $\mathbb R^d$, $d \geq 3$, with drift $b$ in a large class of locally unbounded vector fields that can have critical-order singularities. Covering the entire range of admissible magnitudes
Externí odkaz:
http://arxiv.org/abs/2405.12332
Autor:
Kinzebulatov, D., Semenov, Yu. A.
We obtain gradient estimates on solutions to parabolic Kolmogorov equation with singular drift in a large class. Such estimates allow to construct a Feller evolution family, which is used to construct unique weak solutions to the corresponding stocha
Externí odkaz:
http://arxiv.org/abs/2303.03993
We study the heat kernel of the supercritical fractional diffusion equation with the drift in the critical H\"{o}lder space. We show that such a drift can have point irregularities strong enough to make the heat kernel vanish at a point for all $t>0$
Externí odkaz:
http://arxiv.org/abs/2112.06329
Publikováno v:
Phys. Rev. B 104, 094423 (2021)
We show theoretically that the magnetic ions, randomly distributed in a two-dimensional (2D) semiconductor system, can generate a ferromagnetic long-range order via the RKKY interaction. The main physical reason is the discrete (rather than continuou
Externí odkaz:
http://arxiv.org/abs/2107.11377
Autor:
Kinzebulatov, D., Semenov, Yu. A.
We consider Kolmogorov operator $-\nabla \cdot a \cdot \nabla + b \cdot \nabla$ with measurable uniformly elliptic matrix $a$ and prove Gaussian lower and upper bounds on its heat kernel under minimal assumptions on the vector field $b$ and its diver
Externí odkaz:
http://arxiv.org/abs/2103.11482
Autor:
Kinzebulatov, D., Semenov, Yu. A.
We consider divergence-form parabolic equation with measurable uniformly elliptic matrix and the vector field in a large class containing, in particular, the vector fields in $L^p$, $p>d$, as well as some vector fields that are not even in $L_{\rm lo
Externí odkaz:
http://arxiv.org/abs/2012.02843
Autor:
Kinzebulatov, D., Semenov, Yu. A.
We establish sharp upper and lower bounds on the heat kernel of the fractional Laplace operator perturbed by Hardy-type drift by transferring it to appropriate weighted space with singular weight.
Comment: Few minor typos fixed, added the graph
Comment: Few minor typos fixed, added the graph
Externí odkaz:
http://arxiv.org/abs/2005.11199
Autor:
Kinzebulatov, D., Semenov, Yu. A.
We establish sharp two-sided weighted bounds on the fundamental solution to the fractional Schr\"{o}dinger operator using the method of desingularizing weights.
Comment: Added a comment on the critical case of relative bound \delta=1
Comment: Added a comment on the critical case of relative bound \delta=1
Externí odkaz:
http://arxiv.org/abs/1905.08712
We establish sharp two-sided bounds on the heat kernel of the fractional Laplacian, perturbed by a drift having critical-order singularity, by transferring it to appropriate weighted space with singular weight.
Comment: Improved presentation
Comment: Improved presentation
Externí odkaz:
http://arxiv.org/abs/1904.07363
Autor:
Kinzebulatov, D., Semenov, Yu. A.
We consider the problem of constructing weak solutions to the It\^{o} and to the Stratonovich stochastic differential equations having critical-order singularities in the drift and critical-order discontinuities in the dispersion matrix.
Externí odkaz:
http://arxiv.org/abs/1904.01268