时间：2013年3月18日下午3:00
地点: 下沙校区教学D楼104（理学院党员之家）
报告摘要：
Using a combination of classical ideas, some going back to Sommerfeld a hundred years ago, and more modern techniques, we address a question raised by Dos Santos Ferreira, Kenig and Salo about what are the optimal regions ${\mathcal R}\subset {\mathbb C}$ for which one can have uniform Lebesgue-estimates for solutions of the forced membrane equation, $$(\Delta+\zeta)u=f,$$ as $\zeta$ ranges over ${\mathcal R}$. We confirm, as Sommerfeld reasoned, that properties of the solution $u$ should depend on properties of solutions of the stationary equations $(\Delta+\lambda)u=0$ (the eigenfunctions) and properties of the spectrum (the eigenvalues $-\lambda$ of the Laplacian).
This is joint work with J. Bourgain, P. Shao and X. Yao.
专家简介：
Christopher D. Sogge是美国约翰·霍普金斯大学（Johns Hopkins university）数学系J. J. Sylvester教授，国际数学家大会45分钟报告人，美国总统奖（Presidential Young Investigator Award）获得者，古根海姆奖（Guggenheim Award）获得者，《美国数学杂志》（American Journal of Mathematics）的主编，著名的调和分析和非线性波动方程方面的专家。
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