A new approach to some free boundary problems of the type of jets and cavities for potential flows is introduced. Both potential and Stokes flows are considered. The variable domain problems are relaxed so that they become nonsmooth optimization problems on fixed domains for somewhat singular state equations. State equations are considered, and multivalued generalized gradients of the variational functionals are studied. The method is constructive.
& Svobodny, T.
(1995). Free-Boundary Problems for Potential and Stokes Flows via Nonsmooth Analysis. SIAM Journal on Mathematical Analysis, 26 (3), 633-658.