Carregant...
Fitxers
Tipus de document
ArticleVersió
Versió acceptadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/194026
On global solutions to semilinear elliptic equations related to the one-phase free boundary problem
Títol de la revista
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
Motivated by its relation to models of flame propagation, we study globally Lipschitz solutions of $\Delta u=f(u)$ in $\mathbb{R}^n$, where $f$ is smooth, nonnegative, with support in the interval $[0,1]$. In such setting, any 'blow-down' of the solution $u$ will converge to a global solution to the classical onephase free boundary problem of Alt-Caffarelli. In analogy to a famous theorem of Savin for the Allen-Cahn equation, we study here the $1 \mathrm{D}$ symmetry of solutions $u$ that are energy minimizers. Our main result establishes that, in dimensions $n<6$, if $u$ is axially symmetric and stable then it is $1 \mathrm{D}$.
Citació
Citació
FERNANDEZ-REAL, Xavier, ROS, Xavier. On global solutions to semilinear elliptic equations related to the one-phase free boundary problem. _Discrete and Continuous Dynamical Systems-Series A_. 2019. Vol. 39, núm. 12, pàgs. 6945-6959. [consulta: 25 de gener de 2026]. ISSN: 1078-0947. [Disponible a: https://hdl.handle.net/2445/194026]