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学术报告
学术报告
美国纽约Yeshiva大学数学系主任陈文雄教授报告通知
澳门新葡新京:系统管理员??发布时间:2016-07-05?? 浏览次数:451

应澳门新葡新京官方网站数学系邀请,美国纽约Yeshiva大学数学系主任、终身教授,西北工业大学特聘教授陈文雄教授来澳门新葡新京官方网站数学系短期访问,并大家带来精彩的报告,欢迎数学系师生踊跃参加。报告具体信息如下:

1、题目:Fully nonlinear nonlocal operators

   时间:7151500-1630

   地点:格物楼503

   摘要We consider equations involving fully nonlinear nonlocal operators $$ F_/alpha(u(x))/equiv/,C_{n,/alpha}PV/int_{/mathbb{R}^n}/frac{G(u(x)-u(z))}{|x-z|^{n+/alpha}}dz=f(x,u).$$

We prove a maximum principle and obtain key ingredients for carrying on the method of moving planes, such as narrow region principle and decay at infinity. Then we establish radial symmetry and monotonicity for positive solutions to Dirichlet problems associated to such fully nonlinear fractional order equations in a unit ball and in the whole space, as well as non-existence of solutions on a half space. We believe that the methods develop here can be applied to a variety of problems involving fully nonlinear nonlocal operators. We also investigate the limit of this operator as $/alpha/rightarrow2$ and show that $$ F_/alpha(u(x)) /rightarrow~a(-/Delta{u(x)}) + b|u(x)|^2.$$

 

2、题目:A priori estimates and existence of solutions for fractional equations

   时间:7181000-1130

   地点:诚格物楼503

   摘要:We develop a direct blowing-up and rescaling argument for nonlinear equations involving nonlocal elliptic  operators including the fractional Laplacian. Instead of using the conventional extension method introduced by Caffarelli and Silvestre to localize the problem, we work directly on the nonlocal operator. Using the defining integral, by an elementary approach, we carry on a blowing-up and rescaling argument directly on the nonlocal equations and thus obtain a priori estimates on the positive solutions. Based on this estimate and the Leray-Schauder degree theory, we establish the existence of positive solutions.

We believe that the ideas introduced here can be applied to problems involving more general nonlocal operators.

 

   概况:陈文雄,美国纽约Yeshiva大学终身教授,数学系主任,西北工业大学特聘教授,国际知名的数学家。曾多次获得美国国家科学基金奖。担任Nonlinear Analysis: Theory, Methods & ApplicationsSCI一区)及Communications on Pure and Applied AnalysisSCI两个数学期刊的编辑。研究方向为非线性偏微分方程,目前以分数阶方程为主。

      曾在国际知名数学期刊上发表学术论文60多篇,多数为SCI一区和二区的,其中SCI一区数学期刊上发表的论文有8篇,包括:Annals of Mathematics( 1 );Communications of Pure and Applied Mathematics(2 );Duke Mathematics Journal( 3 )。他在1991 Duke Math. J. 上发表的名为Classification of solutions of some nonlinear elliptic equations一篇被引高达650次以上;在2006 CPAM 上发表的名为 Classification for the solutions of integral equations 一篇被引高达 350 次以上。出版专著《Methods on Nonlinear Elliptic Equations》一本。年底即将出版另一专著《The Fractional Laplacian.

 


 
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