A REMARK ABOUT TARTAR'S LEMMA  

作　　者：ZHANG Weitao FENG Dexing (Institute of Systems Science,Academia Sinica,Beijing 100080,China) 

出　　处：《Systems Science and Mathematical Sciences》1992年第4期312-315,共4页

基　　金：This research was supported by the National Natural Science Foundation of China

摘　　要：Let ■Ω=Γ=Γ₁+Γ₂ （see Fig.1）,meas（Γ₁）】0,V={v|v∈H¹（Ω）,v|Γ₁=0},and V₀={ω|Δω=h in Ω,ω|Γ=0,（?）h∈V}.Let V₀′=thedual space of V₀,a（u,v）=∫_Ω▽u·▽Δvdx,and F（v）=∫_Ω fvdx+∫_Γ₂g1Δvds-∫_Γg2（?）ds,f∈V′₀,g1∈H^-（1/2）（Γ₂）,g2∈H^-（3/2）（Γ）.Consider the variational problem:find u ∈ V such thata（u,v）=F（v）,（?）v∈V₀. （1）Using Tartar’s lemma,we prove that for problem （1） there exists a uniqueLet (?)Ω=Γ=Γ_1+Γ_2 (see Fig.1),meas(Γ_1)>0,V={v|v∈H^1(Ω),v|Γ_1=0},and V_0={ω|Δω=h in Ω,ω|Γ=0,(?)h∈V}.Let V_0′=thedual space of V_0,a(u,v)=∫_Ω▽u·▽Δvdx,and F(v)=∫_Ω fvdx+∫_(Γ_2)g1Δvds-∫_Γg2(?)ds,f∈V′_0,g1∈H^(-(1/2))(Γ_2),g2∈H^(-(3/2))(Γ).Consider the variational problem:find u ∈ V such thata(u,v)=F(v),(?)v∈V_0. (1)Using Tartar's lemma,we prove that for problem (1) there exists a unique u∈Vsatisfying(?)

关 键 词：Tartar’s LEMMA GENERALIZED Poincaré-Friedrichs INEQUALITY 

分 类 号：N94[自然科学总论—系统科学]