A singular perturbation approach to the Dirichlet-area minimisation problem

Anthony Salib, Georg S. Weiss

We study both one and two-phase minimisers of the Dirichlet-area energy $$E(v)={\int }_{B_1}|\nabla v{|}^2+Per(\{v>0\},B_1).$$ In the two-phase case, we show that the energ…