Jingang Xiong

On a fractional Nirenberg problem, part I: Blow up analysis and compactness of solutions

We prove some results on the existence and compactness of solutions of a fractional Nirenberg problem.

On a Fractional Nirenberg Problem, Part II: Existence of Solutions

This paper is a continuation of our earlier work “[T. Jin, Y.Y. Li and J. Xiong, On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, to appear in J. Eur. Math. Soc.]”, where compactness results were given on a fractional Nirenberg problem. We prove two existence results stated there. We also obtain a fractional Aubin inequality.

A Harnack inequality for fractional Laplace equations with lower order terms

We establish a Harnack inequality of fractional Laplace equations without imposing sign condition on the coefficient of zero order term via the Mosers iteration and John-Nirenberg inequality.

Schauder estimates for nonlocal fully nonlinear equations

Abstract In this paper, we establish pointwise Schauder estimates for solutions of nonlocal fully nonlinear elliptic equations by perturbative arguments. A key ingredient is a recursive Evans–Krylov theorem for nonlocal fully nonlinear translation invariant equations.

Schauder estimates for solutions of linear parabolic integro-differential equations

We prove optimal pointwise Schauder estimates in the spatial variables for solutions of linear parabolic integro-differential equations. Optimal Holder estimates in space-time for those spatial derivatives are also obtained.

Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three

We study conformal metrics on

A Liouville Theorem for Solutions of Degenerate Monge-Ampère Equations

{\mathbb {R}}^{3}

A sharp Sobolev trace inequality involving the mean curvature on Riemannian manifolds

R3, i.e., metrics of the form