A minimization problem with free boundary related to a cooperative system
A minimization problem with free boundary related to a cooperative system
We study the minimum problem for the functional ∫Ω(|∇u|2+Q2χ{|u|>0})dx with the constraint ui≥0 for i=1,…,m, where Ω⊂Rn is a bounded domain and u=(u1,…,um)∈H1(Ω;Rm). First we derive the Euler equation satisfied by each component. Then we show that the noncoincidence set {|u|>0} is (locally) nontangentially accessible. Having this, we are able …