摘要
Let ■Ω=Γ=Γ<sub>1</sub>+Γ<sub>2</sub> （see Fig.1）,meas（Γ<sub>1</sub>）】0,V={v|v∈H<sup>1</sup>（Ω）,v|Γ<sub>1</sub>=0},and V<sub>0</sub>={ω|Δω=h in Ω,ω|Γ=0,（?）h∈V}.Let V<sub>0</sub>′=thedual space of V<sub>0</sub>,a（u,v）=∫<sub>Ω</sub>▽u·▽Δvdx,and F（v）=∫<sub>Ω</sub> fvdx+∫<sub>Γ<sub>2</sub></sub>g1Δvds-∫<sub>Γ</sub>g2（?）ds,f∈V′<sub>0</sub>,g1∈H<sup>-（1/2）</sup>（Γ<sub>2</sub>）,g2∈H<sup>-（3/2）</sup>（Γ）.Consider the variational problem:find u ∈ V such thata（u,v）=F（v）,（?）v∈V<sub>0</sub>. （1）Using Tartar’s lemma,we prove that for problem （1） there exists a unique
Let (?)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(?)
基金
This research was supported by the National Natural Science Foundation of China
