
%u minmizes E(u, lambda_1) over set l0={integral(x.*u)./integral(u)=m}

function E_1 = centroidConstraint(u,~)
lambda=[ 1; 0.5; 0.3; 1.5; 0.6; 1; 1.8; 2; 0.2; 0.16; 1.4; 2];
n= lambda(2);
E_1(u,n)=sum(int(f(x)).*u,int(g(x)).* abs(Du(x)))+n.*(int(m-x).*u).^2;
