Constraint maps with free boundaries: the Bernoulli case

Alessio Figalli, André Guerra, Sunghan Kim +1

In this manuscript, we delve into the study of maps $u\in W^{1,2}(\Omega ;\overline{M})$ that minimize the Alt-Caffarelli energy functional $${\int }_{\Omega }(|Du{|}^2+q^2{\chi }_{u^{-1}(M)})dx,$$ u…