39 citations · 503 across the 77 of their papers we have counts for
14 papers · 1 filter
Second order fractional mean-field SDEs with singular kernels and measure initial data
Zimo Hao, Michael Röckner, Xicheng Zhang
In this paper we establish the local and global well-posedness of weak and strong solutions to second order fractional mean-field SDEs with singular/distribution interaction kernel…
Maximum principle for non-uniformly parabolic equations and applications
Xicheng Zhang
In this paper we study the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi's iteration. As applications, we show the existen…
Heat kernels for time-dependent non-symmetric mixed Lévy-type operators
Zhen-Qing Chen, Xicheng Zhang
In this paper we establish the existence and uniqueness of heat kernels to a large class of time-inhomogenous non-symmetric nonlocal operators with Dini's continuous kernels. Moreo…
Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift
S. Menozzi, A. Pesce, X. Zhang
We consider non degenerate Brownian SDEs with H{ö}lder continuous in space diffusion coefficient and unbounded drift with linear growth. We derive two sided bounds for the associat…
Schauder's estimate for nonlocal kinetic equations and its applications
Zimo Hao, Mingyan Wu, Xicheng Zhang
In this paper we develop a new method based on Littlewood-Paley's decomposition and heat kernel estimates of integral form, to establish Schauder's estimate for the following degen…
Dirichlet problem for supercritical nonlocal operators
Xicheng Zhang, Guohuan Zhao
Let be a bounded -domain. Consider the following Dirichlet initial-boundary problem of nonlocal operators with a drift: $$ \partial_t u={\mathscr L}^{(α)}_κu+b\cdot \nabla…