论文标题
$ p $ harmonic功能的混合边界价值问题在无限缸中
Mixed boundary value problem for $p$-harmonic functions in an infinite cylinder
论文作者
论文摘要
我们研究了$ p $ -laplace方程的混合边界价值问题$Δ_pu = 0 $在开放的无限圆形半缸中，并在边界的一部分上有规定的dirichlet边界数据，其余部分的neumann边界数据。对于Sobolev和边界的DIRICHLET部分的连续数据证明了解决混合问题的薄弱解决方案的存在。我们还以适合圆柱体的变异能力来获得无穷大点的边界规则性结果。
We study a mixed boundary value problem for the $p$-Laplace equation $Δ_p u=0$ in an open infinite circular half-cylinder with prescribed Dirichlet boundary data on a part of the boundary and zero Neumann boundary data on the rest. Existence of weak solutions to the mixed problem is proved both for Sobolev and for continuous data on the Dirichlet part of the boundary. We also obtain a boundary regularity result for the point at infinity in terms of a variational capacity adapted to the cylinder.
