Approximation of minimal surfaces with free boundaries (Q1729844)

The authors develop a penalty method to approximate solutions of the free boundary problem for minimal surfaces. For this goal they study the problem of finding minimizers of a certain functional which is defined as the sum of the Dirichlet integral as well as an appropriate penalty term weighted by a parameter \(\lambda\). They show -- among other things -- the existence of a solution when \(\lambda\) is large enough and the convergence to a solution of the free boundary problem in the case when the parameter \(\lambda\) tends to infinity. Regularity at the boundary of these solutions is obtained.