## 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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### References:

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