论文标题
关于$ p $ -laplacian的第二个边界价值问题的解决方案，riemannian歧管
On the existence of solutions of the second boundary value problem for $p$-Laplacian on Riemannian manifolds
论文作者
论文摘要
我们获得了边界价值问题解决方案的必要和足够的存在条件$$ Δ_pu = f \ Quad \ mbox {on} m， \ Quad \左边。 \ left | \ nabla u \ right |^{p -2} \ frac {\ partial u} {\partialν} \ right | _ { \ partial m } = h，$$，其中$ p> 1 $是一个真实的数字，$ m $是带有边界的连接的完整的Riemannian歧管，而$ν$是$ \ partial m $的外部正常矢量。
We obtain necessary and sufficient existence conditions for solutions of the boundary value problem $$ Δ_p u = f \quad \mbox{on } M, \quad \left. \left| \nabla u \right|^{p - 2} \frac{\partial u}{\partial ν} \right|_{ \partial M } = h, $$ where $p > 1$ is a real number, $M$ is a connected oriented complete Riemannian manifold with boundary, and $ν$ is the external normal vector to $\partial M$.
