5 citations · 28 across the 36 of their papers we have counts for
39 papers
Kinetic SDEs and kinetic Fokker-Planck equations with critical Morrey-type drifts, and local blow-ups
Jean-François Jabir, Damir Kinzebulatov, Chengjun Yue
We develop a Sobolev theory for the kinetic Fokker-Planck equation subject to a singular Morrey-form force field which can produce local blow-ups due to strong att…
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…
Strong solutions of SDEs with critical discontinuities in diffusion coefficients
S. E. Boutiah, D. Kinzebulatov
We prove strong existence for Itô SDEs with diffusion coefficients that can introduce strong attraction to a submanifold. We extend and strengthen the Röckner-Zhao approach, which…
Non-local SDEs, critical drifts and local blow-ups
Damir Kinzebulatov, Chengjun Yue
The paper is concerned with -stable SDEs with singular time-inhomogeneous general drift. Our drifts satisfy a condition that is close to the minimal possible scaling-invariance…
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…