报告题目：Integrability, regularity and symmetry of positive solutions for Wolff type integral systems
报告人：张志涛研究员（中国科学院数学与系统科学研究院）
邀请人：罗海军
时间：2024年9月6日16:30-17:30
地点：数学学院207
报告摘要：We are concerned with the optimal integrability, regularity and symmetry of integrable solutions for the Wolff type integral systems. Firstly, we prove the optimal integrability and boundedness of solutions by constructing a nonlinear contracting operator and applying the regularity lifting lemma. Moreover, we exploit the general regularity lifting theorem to derive the Lipschitz continuity as $\gamma>2$. We also prove that the solutions $u$ and $v$ vanish at infinity. The results are valuable for the corresponding$\gamma$-Laplace and $k$-Hessian systems. Secondly, we use the method of moving planes to prove the symmetry and monotonicity of solutions as $\gamma>2$. Minkowski's inequality is crucial in our proofs. We believe that our arguments can be used to prove similar results for other Wolff type integral systems when $\gamma>2$. We also introduce our other new advances on this topic (joint with Yan Bai, Zexin Zhang).
个人简介：张志涛，中国科学院数学与系统科学研究院二级研究员、博士生导师, 华罗庚数学首席研究员，中国科学院特聘研究员（核心骨干），中国科学院大学岗位教授，兼江苏大学数学科学学院院长。国家杰出青年基金获得者、国家领军人才、科技部中青年科技创新领军人才、洪堡学者。长期从事非线性泛函分析理论和应用的前沿研究，Springer出版社出版专著一部，科学出版社出版合著一部，在Journal of Functional Analysis，Annales de l'Institut Henri Poincare Analyse Non Lineaire，J. Differential Equations，Calculus of Variations and PDE, Transactions of American Mathematical Society等著名学术刊物发表论文120多篇，其中SCI 110多篇。在困难的自由边界问题，非线性Schrodinger方程组，生物竞争方程组等方面取得重要成果, 解决了困难的Terracini猜想和3维Henon-Lane-Emden猜想等重要问题。这些成果产生了广泛的影响，被引用2500多次，有的已成为基本参考文献，在研究领域起着引领作用，多次应邀在重要国际会议上作大会报告。曾担任中国数学会副秘书长，担任Springer 期刊Partial Differential Equations and Applications 主编，和DCDS等6个国际刊物编委。
