摘要
对凸角域上的 Neumann问题△ u+au=f inΩ , u n=0 on Ω ,这里 a≥ 0是Ω上的有界可测函数且不恒为 0 ,我们证明了 :若 f∈ L2 (Ω) ,则解 u∈ H2 (Ω) ,且有正则性估计‖ u‖ 2 ,Ω≤ C‖ f‖ 0 ,Ω.
An elliptic Neumann's problem △u+au=f in Ω,un=0 on Ω ,is discussed,where a≥0 is bounded and measurable in Ω ,and does not disappear.If Ω is a conves polygon domain,then the weak solution u∈H 2(Ω) and there is a regularity estimate ‖u‖ 2,Ω ≤C‖f‖ 0,Ω .
出处
《数学理论与应用》
2003年第2期70-73,共4页
Mathematical Theory and Applications
