论文标题
Kellogg的定理用于双线连接的Riemann表面之间的dirichlet能量的差异最小值
Kellogg's theorem for diffeomophic minimisers of Dirichlet energy between doubly connected Riemann surfaces
论文作者
论文摘要
我们将著名的凯洛格定理以形式形态形态形态扩展到Dirichlet Energy的最低限度。就是说，我们证明了diffemorthic的最小化dirichlet sobolev映射的dirichlet能量，在双重连接的riemanian surfaces $（\ x，σ）$和$（\ y，ρ）$中，$ \ mathscr {c}^{c}^{ $ \ mathscr {c}^{n，α} $一直到边界，前提是公制$ρ$足够平稳。这里$ n $是一个积极的整数。至关重要的是，Dirichlet Energy的每个差异最小化都是一个谐波映射，具有非常特殊的HOPF差异，并且此事实用于证明。这改进并扩展了作者和lamel在\ cite {kalam}中的最新结果，在复杂平面中，作者证明了双连接域的结果相似，但以$α'$的价格为$ \ leleα$和$ρ\ equiv 1 $。这是T. iwaniec等人证明的存在结果的补充结果。在\ cite {iwa}和作者in \ cite {kal0}中
We extend the celebrated theorem of Kellogg for conformal diffeomorphisms to the minimizers of Dirichlet energy. Namely we prove that a diffeomorphic minimiser of Dirichlet energy of Sobolev mappings between doubly connected Riemanian surfaces $(\X,σ)$ and $(\Y,ρ)$ having $\mathscr{C}^{n,α}$ boundary, $0<α<1$, is $\mathscr{C}^{n,α}$ up to the boundary, provided the metric $ρ$ is smooth enough. Here $n$ is a positive integer. It is crucial that, every diffeomorphic minimizer of Dirichlet energy is a harmonic mapping with a very special Hopf differential and this fact is used in the proof. This improves and extends a recent result by the author and Lamel in \cite{kalam}, where the authors proved a similar result for double-connected domains in the complex plane but for $α'$ which is $\le α$ and $ρ\equiv 1$. This is a complementary result of an existence result proved by T. Iwaniec et al. in \cite{iwa} and the author in \cite{kal0}
