数値解析・応用解析セミナー

9月25日(火) 15:30 -- 17:00  川越 大輔（Inha University, Korea）
            ``Surface Riesz transforms and spectral property of elastic
              Neumann-Poincar\'e operators on less smooth domains in 3D.''

  ＜研究発表要旨＞
The Neumann-Poincar\'e operator is a boundary integral operator which
naturally appears when we solve classical boundary value problems for
elliptic operators by using layer potentials. It is known that the
elastic Neumann-Poincar\'e operator, which is the Neumann-Poincar\'e
operator for the Lam\'e system of linear elasticity, is polynomially
compact and, as a consequence, that its spectrum consists of three
non-empty sequences of eigenvalues accumulating to certain numbers
determined by Lam\'e parameters, if the boundary of the domain where
the operator is defined is $C^\infty$-smooth.
  In this talk, we extend this result to less smooth boundaries, namely,
$C^{1, \alpha}$-smooth boundaries for some $\alpha$ > 0. The results are
obtained by proving certain identities for surface Riesz transforms,
which are singular integral operators of non-convolution type, defined
by the metric tensor on a given surface.

This talk is based on joint work with Prof. Hyeonbae Kang (Inha University).

●セミナー室: 京都大学 総合研究12号館 2階203号
              （応用解析学講座セミナー室）

●総合研究12号館はキャンパスマップでは「京都大学本部構内 54番建物」です。
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セミナー連絡先: 京都大学大学院 情報学研究科 先端数理科学専攻
                 磯 祐介    e-mail; iso@i.kyoto-u.ac.jp