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讲准字60号:On Ambrosetti-Malchiodi-Ni conjecture on two-dimensional smooth bounded domains

发布时间:2018-04-12|浏览次数:

题目:On Ambrosetti-Malchiodi-Ni conjecture on two-dimensional smooth bounded domains

主讲:杨军

时间:2018年4月16日 9:00

地点:理学院206

主办:理学院


主讲简介:杨军,华中师范大学教授,博士生导师。研究专长:非线性偏微分方程。2007年获得香港中文大学数学哲学博士学位,访问过多个国际著名数学研究中心,主持国家自然科学基金青年项目和面上项目等多个国家课题。主要研究方向是非线性偏微分方程和非线性分析,在多个国际高水平学术期刊上发表论文,如:Geometric and Functional Analysis、 Transactions of the American Mathematical Society、 Indiana University Mathematical Journal、Communications in Partial Differential Equations、SIAM Journal on Mathematical Analysis等。

 

主讲内容:We consider a singularly perturbed elliptic problem on a smooth two dimensional bounded domain. Let $\Gamma$ be a curve intersecting orthogonally with the boundary at exactly two points and dividing the domain into two parts. Moreover, $\Gamma$ satisfies stationary and non-degeneracy conditions with respect to the arc length functional . We prove the existence of a solution concentrating along the whole of $\Gamma$, exponentially small at any positive distance from it, provided that small parameter is small and away from certain critical numbers. In particular, this establishes the validity of the two dimensional case of a conjecture by A. Ambrosetti, A. Malchiodi and W.-M. Ni (p.327, Indiana Univ. Math. J. 53 (2004), no. 2). This is a joint work with Suting Wei, Fang Xiao and Bin Xu.


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