Geodesic
On the full regularity of the free boundary for minima of Alt–Caffarelli functionals in Orlicz spaces
J. Ederson M. Braga1 ; Patrícia R. P. Regis1
1Universidade Federal do Ceará, Departamento de Matemática
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 961-977

Voir la notice de l'article provenant de la source Journal.fi

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 $F(u) := \partial \{ u > 0 \} \cap \Omega$ of minimizers of the Alt-Caffarelli functional $J_G(u) := \int_{\Omega} \left( G(\vert \nabla u \vert) + \lambda \chi_{\{ u > 0 \}} \right) dx$ for suitable N-functions $G$. Next, we prove as a consequence of our main results that there exist a critical dimension $5 \leq n_0 \leq 7$ and a universal constant $\varepsilon_0 \in (0,1)$ such that if $G(t)$ is "$\varepsilon_0$-close" of $t^2$, then for $2 \leq n < n_0$, $F(u)$ is a real analytic hypersurface.  
DOI : 10.54330/afm.120561
Keywords: Full regularity, free boundary problem, Orlicz spaces

J. Ederson M. Braga  1   ; Patrícia R. P. Regis  1

1 Universidade Federal do Ceará, Departamento de Matemática 
J. Ederson M. Braga; Patrícia R. P. Regis. On the full regularity of the free boundary for minima of Alt–Caffarelli functionals in Orlicz spaces. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 961-977. doi: 10.54330/afm.120561
@article{AFM_2022_47_2_a16,
     author = {J. Ederson M. Braga and Patr{\'\i}cia R. P. Regis},
     title = {On the full regularity of the free boundary for minima of {Alt{\textendash}Caffarelli} functionals in {Orlicz} spaces},
     journal = {Annales Fennici Mathematici},
     pages = {961--977},
     year = {2022},
     volume = {47},
     number = {2},
     doi = {10.54330/afm.120561},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.120561/}
}
TY  - JOUR
AU  - J. Ederson M. Braga
AU  - Patrícia R. P. Regis
TI  - On the full regularity of the free boundary for minima of Alt–Caffarelli functionals in Orlicz spaces
JO  - Annales Fennici Mathematici
PY  - 2022
SP  - 961
EP  - 977
VL  - 47
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.54330/afm.120561/
DO  - 10.54330/afm.120561
LA  - en
ID  - AFM_2022_47_2_a16
ER  - 
%0 Journal Article
%A J. Ederson M. Braga
%A Patrícia R. P. Regis
%T On the full regularity of the free boundary for minima of Alt–Caffarelli functionals in Orlicz spaces
%J Annales Fennici Mathematici
%D 2022
%P 961-977
%V 47
%N 2
%U http://geodesic.mathdoc.fr/articles/10.54330/afm.120561/
%R 10.54330/afm.120561
%G en
%F AFM_2022_47_2_a16

Cité par Sources :