Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	代国伟教授，大连理工大学
Inviter:	韩丕功
Title:	Some results of an overdetermined elliptic problem on unbounded domains
Language:	Chinese
Time & Venue:	2023.09.14 16:00-17:00 腾讯会议: 765-735-205
Abstract:	We prove the existence of two smooth families of unbounded domains such that an overdetermined elliptic problem admits a sign-changing solution. The domains bifurcate from the straight cylinder. These results can be regarded as counterexamples to the Berenstein conjecture on unbounded domain. Unlike most previous papers in this direction, a very delicate issue here is that there may be two-dimensional kernel space at some bifurcation point. Thus a Crandall-Rabinowitz type bifurcation theorem from high-dimensional kernel space is also established to achieve the goal. Some other related results on overdetermined elliptic problems are also presented.