论文标题
非本地方程和紧凑型歧管上的最佳Sobolev不平等
Non-local equations and optimal Sobolev inequalities on compact manifolds
论文作者
论文摘要
本文涉及紧凑的riemannian歧管上的分数Sobolev空间。我们证明了临界范围内的Sobolev不平等，对于这些分数Sobolev空间，其最佳常数。我们使用此结果来研究由非局部内部差异算子$ \ Mathcal {l} _ {\ Mathcal {k}} $驱动的方程式的非平凡解的存在。
This paper deals with fractional Sobolev spaces on a compact Riemannian manifold. We prove a Sobolev inequality in the critical range with an optimal constant for these fractional Sobolev spaces. We use this result to study the existence of a non-trivial solution for equations driven by a non-local integro-differential operator $\mathcal{L}_{\mathcal{K}}$ with critical non-linearity.
