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Homepage of Jiguang Bao

基金项目

2020年12月，主持国家重点研发项目课题2020YFA0712904《几何物理方程和种群动力系统》

2019年1月，主持国家自然科学基金项目11871102《拉格朗日平均曲率方程奇点的研究》

2017年1月，参加国家自然科学基金重点项目11631002《几何中的退化与奇异偏微分方程》

2014年1月，主持国家自然科学基金项目11371060《弹性复合材料中偏微分方程组的研究》

2011年1月，主持教育部高等学校博士学科点专项科研基金项目20100003110003《复Monge-Ampère方程的内部正则性和Liouville定理》

2011年1月，主持国家自然科学基金项目11071020《 复合材料中的椭圆和抛物方程》

2008年1月，主持中美数学研究人员交流计划108111202《关于某些非线性椭圆型方程的研究》

2007年1月，Ky and Yu-Fen Fan Fund Award of the American Mathematical Society

2007年1月，主持教育部高等学校博士学科点专项科研基金项目《Alexandrov问题及其推广》

2007年1月，主持国家自然科学基金项目10671022《与平均曲率有关的非线性椭圆方程》

2004年1月，主持教育部重点项目《非线性偏微分方程若干问题的研究》

2004年7月，主持教育部外国文教专家项目《非线性椭圆方程的Liouville性质》

2004年1月，主持国家自然科学基金项目10371011《几何中的非线性偏微分方程》

2003年1月，主持留学回国人员科研启动基金项目《Special Lagrangian方程及其推广》

2000年1月，主持教育部高等学校博士学科点专项科研基金项目《Monge-Ampère方程及其在几何上的应用》

参加5项国家自然科学基金 面上项目(11571042, 11171023, 10071005, 19771009, 19372008)

 

Oct 01, 2013

主要科研论文

  1. PDF (with Ziwei Zhou and Shuyu Gong) Ancient solutions of exterior problem of parabolic Monge-Ampère equations. Ann. Mat. Pura Appl. 200 (2021), no. 4, 1605–1624.

  2. PDF (with Zixiao Liu) Asymptotic expansion at infinity of solutions of Monge-Ampère type equations. Nonlinear Anal. 212 (2021), 112450.

  3. PDF  (with Rongli Huang), Existence and regularity for some degenerate parabolic equation. Differ. Equ. Dyn. Syst. 29 (2021), no. 2, 339–351. 

  4. PDF (with Ziwei Zhou and Bo Wang), A Liouville theorem of parabolic Monge-Ampère equations in half-space. Discrete Contin. Dyn. Syst. 41 (2021), no. 4, 1561–1578. 

  5. PDF (with Limei Dai), Entire solutions of Cauchy problem for parabolic Monge-Ampère equations. Adv. Nonlinear Stud. 20 (2020), no. 4, 769–781. 

  6. PDF (with Yimei Li), Semilinear elliptic system with boundary singularity. Discrete Contin. Dyn. Syst. 40 (2020), no. 4, 2189–2212. 

  7. PDF (with Shuyu Gong and Ziwei Zhou), Existence and uniqueness of viscosity solutions to the exterior problem of a parabolic Monge-Ampère equation. Commun. Pure Appl. Anal. 19 (2020), no. 10, 4921–4936. 

  8. PDF (with Yimei Li), Liouville theorem and isolated singularity of fractional Laplacian system with critical exponents. Nonlinear Anal. 191 (2020), 111636, 24 pp. 

  9. PDF (with Xingchen Pan), A perfect form of inhomogeneous elliptic Equations, Journal of BNU, 56(5) 2020, 629-636.

  10. PDF (with Jingang Xiong and Ziwei Zhou), Existence of entire solutions of Monge-Ampère equations with prescribed asymptotic behavior. Calc. Var. Partial Differential Equations 58 (2019), no. 6, Paper No. 193, 12 pp.

  11. PDF (with Yimei Li) Local behavior of solutions to fractional Hardy–Hénon equations with isolated singularity. Ann. Mat. Pura Appl. 198 (2019), 1, 41–59. 

  12. PDF (with Yimei Li) Fractional Hardy–Hénon equations on exterior domains.  J. Differential Equations, 266 (2019), 1153–1175.

  13. PDF (with Wei Zhang) A Calabi theorem for solutions to the parabolic Monge–Ampère equation with periodic data. Ann. Inst. H. Poincaré Anal. Non Linéaire, 35 (2018), 1143–1173. 

  14. PDF (with Wei Zhang and Bo Wang) An extension of Jörgens–Calabi–Pogorelov theorem to parabolic Monge–Ampère equation,  Calc. Var. Partial Differential Equations, 57(2018), 57-90.

  15. PDF (with Yongjiang Zheng, Qiyi Zhao, Tianshou Zhou and Xiaoqiang Sun) A Spatio-temporal Model of Macrophage-mediated Drug Resistance in Glioma Immunotherapy, Molecular Cancer Therapeutics, 2018: molcanther.0634.2017.

  16. PDF (with Yifei Wu) Global well-posedness for the periodic generalized Korteweg–de Vries equations, Indiana Univ. Math. J. 66 (2017), 1797–1825.

  17. PDF (with Hongjie Ju and Haigang Li) Optimal boundary gradient estimates for Lamé systems with partially infinite coefficients, Adv. Math. 314 (2017), 583–629.

  18. PDF (with Xu Cao) Hessian equations on exterior domain. J. Math. Anal. Appl. 448 (2017), 22–43.

  19. PDF (with Haigang Li and Yanyan Li) Gradient estimates for solutions of the Lame system with partially infinite coefficients in dimensions greater than two, Adv. Math. 305 (2017), 298–338.

  20. PDF (with Xiaoqiang Sun, Zhuhong You, Xing Chen, Jun Cui, Modeling of signaling crosstalk-mediated drug resistance and its implications on drug combination, Oncotarget, 7 (2016), 63995-64006.

  21. PDF (与李美生合作) 极小曲面方程Bernstein定理的一个推广, 中国科学：数学, 46(2016), 513-522.

  22. PDF (with Haigang Li and Lei Zhang) Global solutions and exterior Dirichlet problem for Monge-Ampere equation in R^2, Differential and Integral Equations, 29(2016), 563-582.

  23. PDF (with Xiaoqiang Sun and Yongzhao Shao) Mathematical Modeling of Therapy-induced Cancer Drug Resistance, Scientific RepoRts, March 1, 2016:  6:22498, DOI: 10.1038/srep22498.

  24. PDF (with Nguyen Lam and Guozhen Lu) Polyharmonic equations with critical exponential growth in the whole space R^n, Discrete and Continuous Dynamical Systems, 36 (2016), 577-600.

  25. PDF (with Qianqian Song, H.Wang, Ashok K. Pullikuth, K.Li, L.Miller and Xiaobo Zhou) Systems biology approach to studying proliferation -- dependent prognostic subnetworks in breast cancer, Scientific Reports, August 10, 2015: 5:12981, 14pp.

  26. PDF (with Bo Wang) Over-determined problems for k-Hessian equations in ring-shaped domains, Nonlinear Analysis, 127 (2015), 143-156.

  27. PDF (with Bo Wang) Asymptotic behavior on a kind of parabolic Monge-Ampere equation, Journal of Differential Equations, 259 (2015), 344-370.

  28. PDF (with Haigang Li and Lei Zhang) Monge-Ampere equation on exterior domains, Calculus of Variations and PDE's, 52 (2015), 39-63.

  29. PDF (with Haigang Li and Yanyan Li) Gradient estimates for solutions of the Lame system with partially infinite coefficients, Arch. Rational Mech. Anal. 215 (2015) 307–351.

  30. PDF (with Haigang Li and Yanyan Li) On the exterior Dirichlet problem for Hessian equations, Transactions of the American Mathematical Society, 366 (2014),  6183–6200.

  31. PDF (with Bo Wang and Haigang Li) Determination of the insulated inclusion in conductivity problem and related Eshelby conjecture, Journal of Differential Equations, 257 (2014) 4503-4524 .

  32. PDF (with Bo Wang) Mirror symmetry for a Hessian over-determined problem and its generalization, Communications on Pure and Applied Analysis, 13 (2014), 2305-2316.

  33. PDF (with Haigang Li) The exterior Dirichlet problem for fully nonlinear elliptic equations related to the eigenvalues of the Hessian, Journal of Differential Equations, 256 (2014), 2480-2501.

  34. PDF (with Xiaoqiang Sun, Kyle C. Nelson, King Chuen Li, George Kulik and Xiaobo Zhou)  Systems Modeling of Anti-apoptotic Pathways in Prostate Cancer: Psychological Stress Triggering Synergism Pattern Switch in Drug Combination Therapy. PLOS Computational Biology. 9(12), 2013: e1003358, 13 pp.

  35. PDF (with Wei Zhang) Regularity of very weak solutions for nonhomogeneous elliptic equation, Commun. Contemp. Math. 15 (2013), 1350012, 19 pp.

  36. PDF (with Hua Tan, Kun Wei and Xiaobo Zhou) In silico study on multidrug resistance conferred by I223R/H275Y double mutant neuraminidase, Molecular BioSystems, 9 (2013), 2764-2774.

  37. PDF (with Jingang Xiong) Sharp Regularity for Elliptic Systems Associated with Transmission Problems, Potential Anal., 39 (2013), 169-194.

  38. PDF (with Haigang Li) The exterior Dirichlet problem for special Lagrangian equations in dimensions n\leq4, Nonlinear Anal., 89 (2013), 219-229.

  39. PDF (with Hongjie Ju) On the exterior Dirichlet problem for Monge-Ampere equations, J. Math. Anal. Appl., 405 (2013), 475-483.

  40. PDF (with Xiaoqiang Sun, Yunqing Kang, Yuanyuan Zhang, Yunzhi Yang and Xiaobo Zhou) Modeling vascularized bone regeneration within a porous biodegradable CaP scaffold loaded with growth factors, Biomaterials, 34 (2013), 4971-4981.

  41. PDF (with Chong Wang) Necessary and sufficient conditions on existence and convexity of solutions for Dirichlet problems of Hessian equations on exterior domains. Proc. Amer. Math. Soc. 141 (2013), 1289-1296.

  42. PDF (with Hua Tan, Jing Fan, Jennifer G Dy and Xiaobo Zhou) A Computational model for compressed sensing RNAi cellular screening, BMC Bioinformatics, 2012, 13:337, 13 pages.

  43. PDF (with Haigang Li) Asymptotic estimates for slowly rotating Newtonian stars. Front. Math. China, 7 (2012), 1141–1149.

  44. PDF (with Hua Tan and Xiaobo Zhou) A novel missense-mutation related feature extraction scheme for 'driver' mutation identification, Bioinformatics, 2012, 28(22): 2948-2955.

  45. PDF (with Haigang Li) On the exterior Dirichlet problem for Monge-Ampere equation in dimension two, Nonlinear Analysis, 75 (2012), 6448-6455.

  46. PDF (with Xiaoqiang Sun, Le Zhang, Hua Tan, Costas Strouthos and Xiaobo Zhou) Multi-scale agent-based brain cancer modeling and prediction of TKI treatment response: Incorporating EGFR signaling pathway and angiogenesis, BMC Bioinformatics, 2012, 13:218, 14 pages.

  47. PDF (Xiaoqiang Sun, Jing Su, Tao Peng, Le Zhang, Yuanyuan Zhang, Yunzhi Yang and Xiaobo Zhou) Cytokine combination therapy prediction for bone remodeling in tissue engineering based on the intracellular signaling pathway, Biomaterials, 33 (2012), 8265-8276.

  48. PDF (with Xiaohu Ji and Haigang Li) Existence and nonexistence theorem for entire subsolutions of k-Yamabe type equations, J. Differential Equations, 253 (2012), 2140-2160.

  49. PDF (with Hongjie Ju and Haiyu Jian) Existence for translating solutions of Gauss curvature flow on exterior domains, Nonlinear Anal., 75 (2012), 3629-3640.

  50. PDF (with Limei Dai) Multi-valued solutions to fully nonlinear uniformly elliptic equations, J. Math. Anal. Appl., 389 (2012), 314-321.

  51. PDF (with Wei Zhang) Regularity of very weak solutions for elliptic equation of divergence form, J. Funct. Anal., 262 (2012), 1867-1878.

  52. PDF (with Rongli Huang) The blow up analysis of the general curve shortening flow, Acta Mathematica Sinica, 27 (2011), 2107-2128.

  53. PDF (with Limei Dai) Multi-valued Solutions to Hessian Equations, Nonlinear Differential Equations and Applications, 18 (2011), 447-457.

  54. PDF (with Haigang Li) Euler-Poisson equations related to general rotating compressible fluids,  Discrete and Continuous Dynamical Systems A, 29 (2011), 1085-1096.

  55. PDF (with Limei Dai) On uniqueness and existence of viscosity solutions to Hessian equations in exterior domains, Front. Math. China, 6 (2011), 221–230.

  56. PDF (with Jingang Xiong) The obstacle problem for Monge-Ampère type equations in non- convex domains, Communications on Pure and Applied Analysis, 10 (2011), 59-68.

  57. PDF (with Jingang Xiong) On Jörgens, Calabi, and Pogorelov type theorem and isolated singularities of parabolic Monge-Ampère equations, J. Differential Equations, 250 (2011), 367-385.

  58. PDF (with Haigang Li) Existence of rotating stars with prescribed angular velocity law, Houston J. Math., 37 (2011), 297-309.

  59. PDF (with Xiaohu Ji) Sufficient and necessary conditions on solvability for Hessian inequalities, Proceedings of the American Mathematical Society, 138 (2010), 175-188.

  60. PDF (with Wenmin Sun) New maximum principles for fully nonlinear ODEs of second order, Discrete and Continuous Dynamical Systems, 19 (2007), 813-823.

  61. PDF (with Shumao Liu) The local regularity for strong solutions of the Hessian quotient equation, Journal of Mathematical Analysis and Applications, 303 (2005), 462-476.

  62. PDF Local maximum principle of semilinear nonuniformly elliptic equations and its applications to Hessian equations, Adv. Math. (China), 33(2004), 547-557.

  63. PDF (with Meisheng Li) Smoothness for strong solutions of a Hessian quotient equation, Adv. Math. (China), 33 (2004), 303-315.

  64. PDF (with Jingyi Chen) Optimal regularity of strong solutions for special Lagrangian equations in dimension 3, Indiana Univ. Math. Jour., 52 (2003), 1231-1249.

  65. PDF (with Jingyi Chen, Bo Guan and Min Ji) Liouville property and regularity of a Hessian quotient equation, Amer. J. Math., 125 (2003), 301-316.

  66. PDF Positive solution for semilinear elliptic equations on general domains, Nonlinear Analysis, 53 (2003), 1179-1191.

  67. PDF Fully nonlinear elliptic equations on general bounded domains, Canadian Jour. Math., 54(2002), 1121-1141.

  68. PDF The Dirichlet problem for the degenerate elliptic Monge-Ampère equation, Jour. Math. Anal. Appl., 238 (1999), 166-178.

  69. PDF The regularity of the surface of the Gauss curvature, Science in China, 28 (1998), 613-616.

 

 

 

Jan 22, 2014