熊金钢 - 北京师范大学 - 数学科学学院

个人简介

熊金钢，北京师范大学教授、博导。研究领域为非线性分析（变分法、椭圆与抛物型偏微分方程），解决Berryman和Holland 1980年提出的快速扩散方程正则性猜想；解决Monge-Ampère方程、Yamabe方程以及奇异调和映照中的若干奇点结构问题；开启非局部Nirenberg问题等临界非线性问题的研究。迄今在国际期刊《Amer. J. Math.》, 《J. Eur. Math. Soc.》, 《J. Reine Angew. Math.》，《Proc. London Math. Soc.》等发表论文40余篇，先后获国家优秀青年科学基金和国家杰出青年科学基金资助。担任《Science China Mathematics》青年编委，入选中国青年科技工作者协会。

研究领域

非线性分析与偏微分方程非线性分析（变分法、椭圆与抛物型偏微分方程） Monge-Ampère方程、Yamabe方程以及奇异调和映照中的若干奇点结构问题非局部Nirenberg问题等临界非线性问题

近期论文

查看导师新发文章（温馨提示：请注意重名现象，建议点开原文通过作者单位确认）

1. Optimal regularity and fine asymptotics for the porous medium equation in bounded domains (with T. Jin and X. Ros-Oton). J. Reine Angew. Math. 809 (2024), 269--300. 2. Stability of the separable solutions for a nonlinear boundary diffusion problem (with T. Jin and X. Yang). J. Math. Pures Appl. 183 (2024), 1--43 . 3. 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. 4. Optimal boundary regularity for fast diffusion equations in bounded domains (with T. Jin). Amer. J. Math. 145 (2023), no. 1, 151--220. 5. 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. 6. Isolated singularities of solutions to the Yamabe equation in dimension 6 (with L. Zhang). Int. Math. Res. Not. (IMRN) Vol. 2022, No. 12, 9571–9597. 7. Compactness of conformal metrics with constant $Q$-curvature. I (with Y.Y. Li). Adv. Math. 345 (2019), 116--160. 8. On the isoperimetric quotient over scalar-flat conformal classes (with T. Jin). Comm. Partial Differential Equations 43 (2018), no. 12, 1737--1760. 9. A derivation of the sharp Moser-Trudinger-Onofri inequalities from the fractional Sobolev inequalities. Peking Math J. 1 (2018), no. 2, 221--229. 10. The Nirenberg problem and its generalizations: A unified approach (with T. Jin, Y.Y. Li). Math. Ann. 369 (2017), no. 1-2, 109--151. 11. Schauder estimates for nonlocal fully nonlinear equations (with T. Jin). Annales IHP-ANL. 33 (2016), 1375--1407. 12. Solutions of some Monge-Ampère equations with isolated and line singularities (with T. Jin). Adv. Math. 289 (2016), 114--141. 13. A sharp Sobolev trace inequality involving the mean curvature on Riemannian manifolds (with T. Jin). Trans. Amer. Math. Soc. 367 (2015), 6751--6770. 14. A fractional Yamabe flow and some applications (with T. Jin). J. Reine Angew. Math. 696 (2014), 187--223. 15. 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. 16. 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.

学术兼职

《Science China Mathematics》青年编委中国青年科技工作者协会中国科学：数学 (中、英文版) Analysis in Theory and Applications Annals of Applied Mathematics