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&g...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展开更多
基金This research was supported by the National Natural Science Foundation of China
文摘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
