48 citations · 128 across the 30 of their papers we have counts for
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Strong solutions of stochastic differential equations with coefficients in mixed-norm spaces
Chengcheng Ling, Longjie Xie
By studying parabolic equations in mixed-norm spaces, we prove the existence and uniqueness of strong solutions to stochastic differential equations driven by Brownian motion with…
Blowup solutions of Grushin's operator
Guangying Lv, Jinlong Wei, Longjie Xie
In this note, we consider the blowup phenomenon of Grushin's operator. By using the knowledge of probability, we first get expression of heat kernel of Grushin's operator. Then by…
Heat kernels for non-symmetric diffusion operators with jumps
Zhen-Qing Chen, Eryan Hu, Longjie Xie +1
For , we establish the existence and uniqueness of heat kernels for a large class of time-dependent second order diffusion operator with jumps, which is the sum of time-de…
Heat kernel estimates for critical fractional diffusion operator
Longjie Xie, Xicheng Zhang
In this work we construct the heat kernel of the 1/2-order Laplacian perturbed by the first-order gradient term in Hölder space and the zero-order potential term in generalized Kat…