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


报告人:徐斌  (江苏师范大学)


  : 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 ( Indiana Univ. Math. J 53(2), 297-329, 2004). This is a joint work with Suting Wei, Jun,Yang.



  间:2018年11月30日 10:00-12:00




邀请人:陈学长 老师