On Elliptic Extensions in the Disk |
| |
Authors: | Cristina Giannotti Paolo Manselli |
| |
Institution: | (1) Ufa State Aviation Technical University, Karl Marx str. 12, Ufa, Russia |
| |
Abstract: | Given two arbitrary functions f (0), f (1) on the boundary of the unit disk D in \({\mathbb R}^2\), it is shown that there exists a second order uniformly elliptic operator L and a function v in L p , with L p second derivatives (1?p?2 ), satisfying Lv?=?0 a.e. in D and with v?=?f (0) and \(\frac{ \partial v}{\partial n} = f^{(1)}\) on \(\partial{D}\). A similar extension property was proved in Cavazzoni (2003) for any pair of functions f (0), f (1) that are analytic; a result is obtained under weaker regularity assumptions, e.g. with \(\frac{\partial f^{(0)}}{\partial \theta}\) and f (1) Hölder continuous with exponent \(\eta > \frac{1}{2}\). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|