On the full regularity of the free boundary for minima of Alt–Caffarelli functionals in Orlicz spaces

Authors

  • J. Ederson M. Braga Universidade Federal do Ceará, Departamento de Matemática
  • Patrícia R. P. Regis Universidade Federal do Ceará, Departamento de Matemática

Keywords:

Full regularity, free boundary problem, Orlicz spaces

Abstract

In this paper, we discuss two issues about the full regularity of the free boundary for overdetermined Bernoulli-type problems in Orlicz spaces. First, we show that in dimension n=2 there are no singular points on the free boundary F(u):={u>0}Ω of minimizers of the Alt-Caffarelli functional
JG(u):=Ω(G(|u|)+λχ{u>0})dx

for suitable N-functions G. Next, we prove as a consequence of our main results that there exist a critical dimension 5n07 and a universal constant ε0(0,1) such that if G(t) is "ε0-close" of t2, then for 2n<n0, F(u) is a real analytic hypersurface.

 

Section
Articles

Published

2022-07-07

How to Cite

Braga, J. E. M., & Regis, P. R. P. (2022). On the full regularity of the free boundary for minima of Alt–Caffarelli functionals in Orlicz spaces. Annales Fennici Mathematici, 47(2), 961–977. https://doi.org/10.54330/afm.120561