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講演会
過去の記録 ～04/19｜次回の予定｜今後の予定 04/20～
2008年05月19日(月)
16:00-17:30 数理科学研究科棟(駒場) 126号室
Jean-Pierre Puel 氏
氏 (ヴェルサイユ大学 (Universite de Versailles St Quentin)
)
A non standard unique continuation property related to Schiffer conjecture
https://www.ms.u-tokyo.ac.jp/top/general-access.html
Jean-Pierre Puel 氏
氏 (ヴェルサイユ大学 (Universite de Versailles St Quentin)
)
A non standard unique continuation property related to Schiffer conjecture
[ 講演概要 ]
Coming from a control problem for a coupled fluid-structure system, we are confronted to the following problem in dimension 2:
\\Delta^2 w = -\\lambda \\Delta w in \\Omega w = {\\partial w}/{\\partial n} = 0 on \\Gamma {\\partial\\Delta w}/{\\partial n}=0 on \\Gamma_0 \\subset \\Gamma.
The question is : do we have w=0?
There is a counterexample when \\Omega is a disc. The analogous of (local) Schiffer's conjecture is : is the disc the only domain for which we can have a non zero solution?
Notice that the term local means that the additional boundary condition occurs only on a part of the boundary and when this boundary is not analytic, this is a major difference. A sub-conjecture would be : when the boundary is not analytic, do we have w=0?
Here we show that when \\Omega has a corner of angle \\theta_{0} with \\theta_{0} \\neq \\pi, 3\\pi/2 and when $\\Gamma_{0}$ is (locally) one edge of this angle then the only solution is w=0.
[ 参考URL ]Coming from a control problem for a coupled fluid-structure system, we are confronted to the following problem in dimension 2:
\\Delta^2 w = -\\lambda \\Delta w in \\Omega w = {\\partial w}/{\\partial n} = 0 on \\Gamma {\\partial\\Delta w}/{\\partial n}=0 on \\Gamma_0 \\subset \\Gamma.
The question is : do we have w=0?
There is a counterexample when \\Omega is a disc. The analogous of (local) Schiffer's conjecture is : is the disc the only domain for which we can have a non zero solution?
Notice that the term local means that the additional boundary condition occurs only on a part of the boundary and when this boundary is not analytic, this is a major difference. A sub-conjecture would be : when the boundary is not analytic, do we have w=0?
Here we show that when \\Omega has a corner of angle \\theta_{0} with \\theta_{0} \\neq \\pi, 3\\pi/2 and when $\\Gamma_{0}$ is (locally) one edge of this angle then the only solution is w=0.
https://www.ms.u-tokyo.ac.jp/top/general-access.html
