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| seminar:2014:018 [2017/11/13 17:22] – 作成 wikiadm | seminar:2014:018 [2017/11/16 18:25] (現在) – 外部編集 127.0.0.1 | ||
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| ==== 第18回 ==== | ==== 第18回 ==== | ||
| + | <WRAP center round box 90%> | ||
| + | * 講演者 : **Der-Chen Chang** 氏（Georgetown 大学） | ||
| + | * 題目：Estimates for elliptic boundary valued problem in Hardy spaces | ||
| + | * 日時：平成27 年3 月9 日（月）16: | ||
| + | </ | ||
| + | |||
| + | |||
| + | Let \(\Omega\) be a bound domain in \(\mathbb{R}^n\) with smooth boundary. | ||
| + | Consider the following elliptic boundary valued problem: | ||
| + | |||
| + | \[ | ||
| + | \begin{cases} | ||
| + | \Delta u = f \quad \text{in}\; \Omega\\ | ||
| + | Xu = g\quad \text{on the boundary}\\ | ||
| + | \end{cases} | ||
| + | \] | ||
| + | Here \(X\) is a transversal vector field to the boundary. | ||
| + | This includes the regular Dirichlet and Neumann problem. | ||
| + | In this talk, we first introduce suitable Hardy spaces \(H_p(\Omega)\) on \(\Omega\). | ||
| + | Then we shall show the inequality | ||
| + | \[ | ||
| + | \text{norm of second partial differential of $f$} \leq \text{const * norm of $f$} | ||
| + | \] | ||
| + | ---- photogallery show ---- | ||
| + | namespace | ||
| + | ---- | ||
| + | |||
| + | [<6>] | ||