5 citations · 28 across the 36 of their papers we have counts for
19 papers · 1 filter
Uniform many-particle spectral gap inequality and heat kernel bounds for strong attractive interactions
S. E. Boutiah, D. Kinzebulatov, K. R. Madou
We prove a spectral gap inequality for Gaussian measures modified by singular attractive pair interactions. The spectral gap constant is explicit and uniform in the number of parti…
Intrinsic Hardy inequality for fractional Kolmogorov operator
Damir Kinzebulatov
We obtain Hardy inequality for non-local diffusion operator with singular drift, in the case when the strength of attraction to the origin by the drift takes the critical value.
Non-local parabolic equations with singular (Morrey) time-inhomogeneous drift
Damir Kinzebulatov
We obtain Sobolev regularity estimates for solutions of non-local parabolic equations with locally unbounded drift satisfying some minimal assumptions. These results yield Krylov b…
Laplacian with singular drift in a critical borderline case
Damir Kinzebulatov
We establish well-posedness and regularity for parabolic diffusion equation in the case when the singularities of a general drift reach the critical magnitude. The latter dictates…
Remarks on parabolic Kolmogorov operator
D. Kinzebulatov, Yu. A. Semenov
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…
On divergence-free (form-bounded type) drifts
Damir Kinzebulatov, Reihaneh Vafadar
We develop regularity theory for elliptic Kolmogorov operator with divergence-free drift in a large class (or, more generally, drift having singular divergence). A key step in our…