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Monotonicity and symmetry of solutions of \(p\)-Laplace equations, \(1<p<2\), via the moving plane method. (English) Zbl 0930.35070
The authors deal with the monotonicity and symmetry properties of solutions of the boundary value problem \[ \begin{cases} -\text{div}(|Du|^{p- 2}Du)= f(u)\quad &\text{in }\Omega,\\ u>0\quad &\text{in }\Omega,\\ u= 0\quad &\text{on }\partial\Omega,\end{cases} \] where \(\Omega\) is a bounded domain in \(\mathbb{R}\), \(N\geq 2\), \(1< p< 2\), and \(f\) is locally Lipschitz continuous. Using the previous results of the first author and the “moving plane method” they are able to show for instance that if \(\Omega\) is a ball then the solutions are radially symmetric and strictly radially decreasing.
Reviewer: V.Mustonen (Oulu)

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35B50 Maximum principles in context of PDEs
35J60 Nonlinear elliptic equations
35J70 Degenerate elliptic equations
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