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(中国科博鱼网页版官网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:数学博鱼网页版官网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,中国科博鱼网页版官网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,中国科博鱼网页版官网特聘研究员(核心骨干),中国科博鱼网页版官网大学岗位教授,兼江苏大学数学科学博鱼网页版官网院长。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。