Harmonic Analysis Komaba Seminar

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Date, time & place Saturday 13:00 - 18:00 128Room #128 (Graduate School of Math. Sci. Bldg.)

2012/11/10

13:00-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Tokio Matsuyama (Chuo University) 13:00-14:20
Perturbed Besov spaces by short-range type potential
in exterior domains (JAPANESE)
[ Abstract ]
In this talk we will define perturbed Besov spaces by a short-range potential over exterior domains. These spaces will be available for obtaining the Strichartz estimates of wave equation with a potential in exterior domains.
We will pay attention to observe the equivalence relation between the perturbed Besov spaces and the free ones.
Sugimoto Mitsuru (Nagoya University) 14:40-16:00
Optimal constants and extremisers for some smoothing estimates (JAPANESE)
[ Abstract ]
Our purpose is to study the optimal constant and extremising initial data for a broad class of smoothing estimates for solutions of linear dispersive equations.
Firstly, we discuss the existence/nonexistence of extremisers and then we provide an explicit formula and new observations for the optimal constant.
The talk is based on joint work with Neal Bez (University of Birmingham).
Victor I. Burenkov (Russia/United Kingdom) 16:30-17:50
Spectral stability of the p-Laplacian (JAPANESE)
[ Abstract ]
Dependence of the eigenvalues of the p-Laplacian upon domain perturbation will be under discussion. Namely Lipschitz-type estimates for deviation of the eigenvalues following a domain perturbation will be presented. Such estimates are obtained for the class of open sets admitting open sets with arbitrarily strong degeneration and are expressed in terms of suitable measures of vicinity of two open sets, such as the \\lq\\lq atlas distance" between these sets or the \\lq\\lq lower Hausdor-Pompeiu
deviation" of their boundaries. In the case of open sets with Holder continuous boundaries, our results essentially improve a result known for the rst eigenvalue [2].
Joint work with P. D. Lamberti. The results were recently published in [1].
Supported by the grant of RFBR (project 08-01-00443).

References:
[1] V.I. Burenkov, P.D. Lamberti, Spectral stability of the p-Laplacian, Nonlinear Analysis, 71, 2009, 2227-2235.
[2] J. Fleckinger, E.M. Harrell and F. de Thelin, Boundary behaviour and estimates for solutions for equations containing the p-Laplacian, Electronic Journal of Dierential Equations, 38, 1999, 1-19.