标题： 最优收敛速率的有限元近似 Sobolev 常数 显示英文标题

标题： Optimal convergence rates for the finite element approximation of the Sobolev constant

摘要： 我们建立了在任意维数 N\geq 2 和 Lebesgue 指数 1<p<N 下 Sobolev 常数的 P1 有限元逼近的最优收敛率。 我们的分析依赖于对适当准范数中 Sobolev 缺陷的深入研究，这些准范数已在 p-Laplacian 的有限元逼近背景下被引入和使用。 证明进一步涉及对 Sobolev 极小值的有限元逼近的精确估计。 显示英文摘要

摘要： We establish optimal convergence rates for the P1 finite element approximation of the Sobolev constant in arbitrary dimensions N\geq 2 and for Lebesgue exponents 1<p<N. Our analysis relies on a refined study of the Sobolev deficit in suitable quasi-norms, which have been introduced and utilized in the context of finite element approximations of the p- Laplacian. The proof further involves sharp estimates for the finite element approximation of Sobolev minimizers.