Sobre a regularidade ótima da fronteira livre para minimizantes de funcionais do tipo Alt-Caffarelli em espaços de Orlicz

Abstract

In this thesis work we discuss two questions about the optimal regularity of the free boundary for Bernoulli-type problems in Orlicz spaces. First, we show that for dimension n = 2 there are no singular points on the minimizer free boundary of Alt-Caffarelli functionals for suitable N-functions G. Next, we prove as a consequence of the main results that there is a critical dimension n0 ≥ 3 and a universal constant ε0 ∈ (0,1) such that if G(t) is ε0-close to t2 then, for 2 ≤ n < n0, F(u) is a real analytic hypersurface.