Category:解析セミナー

日　　　時：　4 月 30 日（水）　15時30分～17時

講　演 者：　Alexandru DIMCA 氏　（University of Nice Sophia Antipolis）

題　　　目：　D-modules and projective hypersurfaces with isolated singularities

講演要旨は　こちら　をご覧ください．

日時: 2014年3月5日(水) 15:00～17:30
場所: 自然系学系棟 D509

15:00～15:50  Jean Vaillant 氏 （パリ第６大学）
Necessary and sufficient conditions of hyperbolicity for linear differential systems.

16:00～17:30  伊藤 健一 氏 (筑波大学)
Threshold properties of one-dimensional discrete Schrödinger operators.
(講演の概要はこちら をご覧ください.)

http://www.math.tsukuba.ac.jp/~analysis/

日　　時：　２月１８日（火）１５時３０分～１７時００分
（曜日が通常と異なりますので，ご注意ください．）

講 演 者：　Elmar Schrohe 氏 （Leibniz Universit\"at Hannover)

題　　目：　Solvability of a Degenerate Boundary Value Problem

要　　旨：　Following work of K.\ Taira we consider the boundary value problem
$$Au=f\text{ in } X,\qquad Lu=g \text{ on }\partial X,$$
where $X$ is a compact manifold with boundary,
$A$ is a strongly elliptic second order operator which in local coordinates is of the form
$$A=\sum_{jk}a^{jk}\partial_{x_j}\partial_{x_k}+\sum b^j\partial_{x_j} + c$$
with real coefficients $a^{jk}=a^{jk}, b^j,c$ in the Htlder class $C^\tau$, $\tau>2$.
We require that
$\sum a^{jk}\xi_j\xi_k\ge \alpha |\xi|^2$ for some $\alpha>0$ and  $0\not\equiv c\le0$.

The  boundary condition $L$ is assumed to be of the form
$$Lu = \mu_0\gamma_0u + \mu_1\gamma_1u,$$
where $\gamma_0$ is the evaluation map at the boundary
and $\gamma_1$ is the evaluation of the exterior normal derivative at the boundary.
The $C^\tau$-functions $\mu_0$ and $\mu_1$ on $\partial X$
are supposed to be nonnegative with $\mu_0+\mu_1$ strictly positive everywhere.

Using the calculus of pseudodifferential operators with symbols of limited regularity
we then show the solvability of the boundary value problem
in various classes of Sobolev and Zygmund spaces with regularity
depending on the smoothness $\tau$ of the coefficients.
We also study the resolvent in suitable sectors of the complex plane.

\hfill (joint work with M. Hassan Zadeh)

【 場所 】 自然学系Ｄ棟　５０９教室

日　　時：　１月１６日（木）１５時３０分～１７時００分
（曜日が通常と異なりますので，ご注意ください．）

講 演 者：　Victor Isakov 氏 （Wichita State University)

題　　目：　On increasing stability in the Cauchy and inverse problems for the
Helmholtz type elliptic equations

要　　旨：　We derive conditional stability estimates for the Helmholtz type equations
which are becoming of Lipschitz type for large frequencies/wave numbers.
Proofs use splitting solutions into low and high frequencies parts where we use energy
(in particular) Carleman estimates. We discuss numerical confirmation and open problems.

We report on new stability estimates for recovery of the near field from the scattering
amplitude and for Schroedinger potential from the Dirichlet-to Neumann map. In these
estimates unstable (logarithmic part) goes to zero as the wave number grows. Proofs
are using new bounds for Hankel functions and complex and real geometrical optics solutions.

【 場所 】 自然学系Ｄ棟　５０９教室