Tianling Jin

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.

Pathological solutions to elliptic problems in divergence form with continuous coefficients

We construct a function u is an element of W-loc(1.1) (B(0, 1)) which is a solution to div(A del u) = 0 in the sense of distributions, where A is continuous and u is not an element of W-loc(1.p) (B(0, 1)) for p > 1. We also give a function u is an element of W-loc(1.1)(B(0, 1)) such that u is an element of W-loc(1.p) (B(0, 1)) for every p < infinity, u satisfies div(A del u) = 0 with A continuous but u is not an element of W-loc(1.infinity) (B(0, 1)). This answers questions raised by H. Brezis (On a conjecture of J. Serrin, Rend. Lincei Mat. Appl. 19 (2008) 335-338). To cite this article: T Jin et al., C. R. Acad. Sci. Paris., Ser. 1 347 (2009)

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.

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

Minimizers for the fractional Sobolev inequality on domains

{\mathbb {R}}^{3}

A Liouville Theorem for Solutions of Degenerate Monge-Ampère Equations

R3, i.e., metrics of the form