三维L_p和L_∞模的离散Sobolev不等式

THREE-Dimensional Discrete Sobolev’s Inequalities in L_p and L_∞ Norms

离散的Sobolev不等式在差分方法理论中特别是在证明差分格式稳定性和收敛性时是重要的工具.在[1—3]中,讨论了一维离散的不等式和插值公式;[4]证明了一些L_p模的离散不等式.为了研究非线性偏微分方程解法,需要多维L_∞模的离散Sobolev不等式.本文在L_ρ模不等式的基础上证明了三维L_∞模Sobolev不等式.

The three-dimensional discrete Sobolev's inequalities in L_p and L_∞ norms areproved by using the discrete Holder inequality and complicated deduction.