Boundary regularity in the Dirichlet problem for the invariant Laplacians <IMG BORDER="0" SRC="/proc/2004-132-11/S0002-9939-04-07582-3/gif-title0/img1.gif" > on the unit real ball期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Boundary regularity in the Dirichlet problem for the invariant Laplacians on the unit real ball

Authors:	Congwen Liu Lizhong Peng

Institution:	School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China ; School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China

Abstract:	We study the boundary regularity in the Dirichlet problem of the differential operators $\begin{displaymath}\Delta_{\gamma}= (1-\vert x\vert^2)\bigg\{ \frac {1-\vert x\v... ...}{\partial x_j} + \gamma\Big(\frac n2 -1 -\gamma \Big)\bigg\}. \end{displaymath}$ Our main result is: if $\gamma>-1/2$ is neither an integer nor a half-integer not less than , one cannot expect global smooth solutions of $\Delta_\gamma u=0$ ; if $u\in C^{\infty}(\overline{B}_n)$ satisfies $\Delta_\gamma u=0$ , then must be either a polynomial of degree at most $2\gamma+2-n$ or a polyharmonic function of degree $\gamma+1$ .

Keywords:	Invariant Laplacians Laplace-Beltrami operator Weinstein equation boundary regularity polyharmonicity

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