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- W1857014730 abstract "We use the method of Alexandroff-Serrin to establish the spherical symmetry of the ground domain and of the weak solution to a free boundary problem for a class of quasi-linear parabolic equations in an unbounded cylinder $Omega times (0,T)$, where $Omega = (mathbb {R}^{n} backslash overline {Omega _{1}})$, with $Omega _{1}subset mathbb R^n$ a simply connected bounded domain. The equations considered are of the type $u_{t} - div (a(u,|Du|)Du) = c(u,|Du|)$, with $a$ modeled on $|Du|^{p-2}$. We consider a solution satisfying the boundary conditions: $u(x,t)=f(t)$ for $(x,t)in partial Omega _{1} times (O,T)$, and $u(x,0)=0$, $urightarrow 0$ as $|x|rightarrow infty$. We show that the overdetermined co-normal condition $a(u,|Du|)frac {partial u}{partial nu }=g(t)$ for $(x,t)in partial Omega _{1} times (O,T)$, with $g(overline T) > 0$ for at least one value $overline T in (0,T)$, forces the spherical symmetry of the ground domain and of the solution." @default.
- W1857014730 created "2016-06-24" @default.
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- W1857014730 date "2001-06-28" @default.
- W1857014730 modified "2023-09-23" @default.
- W1857014730 title "Symmetry in a free boundary problem for degenerate parabolic equations on unbounded domains" @default.
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- W1857014730 doi "https://doi.org/10.1090/s0002-9939-01-05993-7" @default.
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