Jingang Xiong (ܽ)

Professor
School of Mathematical Sciences
Beijing Normal University

   







Contact Information

Address     Main Building 1216, School of Mathematical Sciences,
Beijing Normal University, Beijing 100875, China
Email jx@bnu.edu.cn

Curriculum Vitae

İ     English Version

Preprints & Publications
  1. Holder regularity for the linearized porous medium equation in bounded domains (with T. Jin). Preprint. arXiv
  2. Asymptotic analysis of harmonic maps with prescribed singularities (with Q. Han, M. Khuri and G. Weinstein). Preprint. arXiv
  3. Stability of the separable solutions for a nonlinear boundary diffusion problem (with T. Jin and X. Yang). Preprint. arXiv
  4. Optimal regularity and fine asymptotics for the porous medium equation in bounded domains (with T. Jin and X. Ros-Oton). Preprint. arXiv
  5. Regularity of viscosity solutions of the $\sigma_k$-Loewner-Nirenberg problem (with Y.Y. Li and L. Nguyen). Proc. London Math. Soc. 127 (2023), no. 4, 1--34. arXiv
  6. Regularity of solutions to the Dirichlet problem for fast diffusion equations (with T. Jin). Preprint. arXiv
  7. Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric (with Z.-C. Han and L. Zhang). J. Funct. Anal. 285 (2023), 109982. arXiv
  8. Bubbling and extinction for some fast diffusion equations in bounded domains (with T. Jin). Trans. Amer. Math. Soc. Ser. B 10 (2023), 1287--1332. arXiv
  9. Blow up limits of the fractional Laplacian and their applications to the fractional Nirenberg problem (with X. Du, T. Jin and H. Yang). Proc. Amer. Math. Soc. 151 (2023), no. 11, 4693--4701. arXiv
  10. Optimal boundary regularity for fast diffusion equations in bounded domains (with T. Jin). Amer. J. Math. 145 (2023), no. 1, 151--220. arXiv
  11. Singular extinction profiles of solutions to some fast diffusion equations (with T. Jin). J. Funct. Anal. 283 (2022), 109595. arXiv
  12. Isolated singularities of solutions to the Yamabe equation in dimension 6 (with L. Zhang). Int. Math. Res. Not. (IMRN) Vol. 2022, No. 12, 9571C9597. arXiv
  13. On a Rayleigh-Faber-Krahn inequality for the regional fractional Laplacian (with T. Jin and D. Kriventsov). Ann. Appl. Math. 37 (2021), 363--393. arXiv
  14. Sharp Sobolev inequalities involving boundary terms revisited (with Z. Tang and N. Zhou).Calc. Var. Partial Differential Equations 60 (2021), no. 6, Paper No. 160, 26 pp. arXiv
  15. Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities (with T. Jin). Ann. Inst. Henri Poincare, Analyse Nonlineaire 38 (2021), 1167--1216. arXiv
  16. Existence of entire solutions of Monge-Ampre equations with prescribed asymptotic behaviors (with J. Bao, Z. Zhou). Calc. Var. Partial Differential Equations 58 (2019), no. 6, Paper No. 193, 12 pp. arXiv
  17. Compactness of conformal metrics with constant $Q$-curvature. I (with Y.Y. Li). Adv. Math 345 (2019), 116--160. arXiv
  18. On the isoperimetric quotient over scalar-flat conformal classes (with T. Jin). Comm. Partial Differential Equations 43 (2018), no. 12, 1737--1760. arXiv
  19. A derivation of the sharp Moser-Trudinger-Onofri inequalities from the fractional Sobolev inequalities. Peking Math J. 1 (2018), no. 2, 221--229. arXiv
  20. On a conformally invariant integral equation involving Poisson kernel. Acta Mathematica Sinica, English Series 34 (2018), no. 4, 681--690. arXiv
  21. Minimizers for the fractional Sobolev inequality on domains (with R. L. Frank, T. Jin). Calc. Var. Partial Differential Equations 57 (2018), no. 2, Art. 43, 31 pp. arXiv
  22. Compactness of solutions to nonlocal elliptic equations (with M. Niu, Z. Peng). J. Funct. Anal. 275(2018), 2333--2372. arXiv
  23. The critical semilinear elliptic equation with boundary isolated singularities. J. Differential Equations 263 (2017), no. 3, 1907--1930.
  24. On local behavior of singular positive solutions to nonlocal elliptic equations (with T. Jin, O S. de Queiroz, Y. Sire). Calc. Var. Partial Differential Equations 56 (2017), no. 1, Art. 9, 25 pp. arXiv
  25. Classification theorems for solutions of higher order boundary conformally invariant problems, I (with L. Sun). J. Funct. Anal. 271 (2016), 3727--3764. arXiv
  26. The Nirenberg problem and its generalizations: A unified approach (with T. Jin, Y.Y. Li). Math. Ann. 369 (2017), no. 1-2, 109--151. arXiv
  27. Schauder estimates for nonlocal fully nonlinear equations (with T. Jin). Ann. Inst. Henri Poincare, Analyse Nonlineaire. 33 (2016), 1375--1407. arXiv
  28. Schauder estimates for solutions of linear parabolic integro-differential equations (with T. Jin). Discrete Contin. Dyn. Syst. 35 (2015), no 12, 5977--5998.
  29. Solutions of some Monge-Amp\`ere equations with isolated and line singularities (with T. Jin). Adv. Math 289 (2016), 114--141.
  30. Boundary Gradient Estimates for Parabolic and Elliptic Systems from Linear Laminates (with H. Dong). Int. Math. Res. Not. (IMRN) 2015 (2015), 7734--7756.
  31. A sharp Sobolev trace inequality involving the mean curvature on Riemannian manifolds (with T. Jin). Trans. Amer. Math. Soc. 367 (2015), 6751--6770.
  32. On a fractional Nirenberg problem, part II: existence of solutions (with T. Jin, Y.Y. Li). Int. Math. Res. Not. (IMRN) 2015 (2015), no. 6, 1555--1589.
  33. Existence and asymptotics for solutions of a non-local $Q$-curvature equation in dimension three (with T. Jin, A. Maalaoui, L. Martinazzi). Calc. Var. Partial Differential Equations 52 (2015), no. 3-4, 469--488.
  34. A fractional Yamabe flow and some applications (with T. Jin). J. Reine Angew. Math. 696 (2014), 187--223.
  35. On a fractional Nirenberg problem, part I: blow up analysis and compactness of solutions (with T. Jin, Y.Y. Li). J. Eur. Math. Soc. (JEMS) 16 (2014), no. 6, 1111--1171.
  36. Local analysis of solutions of fractional semi-linear elliptic equations with isolated singularities (with L. Caffarelli, T. Jin, Y. Sire). Arch. Ration. Mech. Anal. 213 (2014), no. 1, 245--268.
  37. A Liouville theorem for solutions of degenerate Monge-Amp\`ere equations (with T. Jin). Comm. Partial Differential Equations 39 (2014), no. 2, 306--320.
  38. Sharp constants in weighted trace inequalities on Riemannian manifolds (with T. Jin). Calc. Var. Partial Differential Equations 48 (2013), no. 3-4, 555--585.
  39. Sharp regularity for elliptic systems associated with transmission problems (with J. Bao). Potential Anal. 39 (2013), no. 2, 169--194.
  40. $C^{1,1}$ estimates for elliptic equations with partial and piecewise continuous coefficients. Methods Appl. Anal. 18 (2011), no. 4, 373--389.
  41. A Harnack inequality for fractional Laplace equations with lower order terms (with J. Tan). Discrete Contin. Dyn. Syst. 31 (2011), no. 3, 975--983.
  42. The obstacle problem for Monge-Amp\`ere type equations in non-convex domains (with J. Bao). Commun. Pure Appl. Anal. 10 (2011), no. 1, 59--68.
  43. On J\"orgens, Calabi, and Pogorelov type theorem and isolated singularities of parabolic Monge-Amp\`ere equations (with J. Bao). J. Differential Equations 250 (2011), no. 1, 367--385.

Last update: September, 2023