An Optimization Problem with Volume Constraint
Néstor E. Aguilera, Hans Wilhelm Alt, Luis A. Caffarelli · SIAM Journal on Control and Optimization · 1986
We consider the optimization problem of minimizing Dirichlet integral $\int_\Omega {| { abla u} |^2 } $ with volume constraint on the set $\{ u > 0\} $. We use a penalization method which for small values of the penalization parameter ; leads to a solution of the original problem.