Monotonicity and symmetry of solutions of \(p\)-Laplace equations, \(1<p<2\), via the moving plane method (Q1287007)
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scientific article; zbMATH DE number 1281955
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Monotonicity and symmetry of solutions of \(p\)-Laplace equations, \(1<p<2\), via the moving plane method |
scientific article; zbMATH DE number 1281955 |
Statements
Monotonicity and symmetry of solutions of \(p\)-Laplace equations, \(1<p<2\), via the moving plane method (English)
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31 October 1999
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Summary: We present some monotonicity and symmetry results for positive solutions of the equation \[ -\text{div}(| Du|^{p- 2}Du)= f(u) \] satisfying a homogeneous Dirichlet boundary condition in a bounded domain \(\Omega\). We assume \(1<p<2\) and \(f\) locally Lipschitz continuous and we do not require any hypothesis on the critical set of the solution. In particular, we get that \(\Omega\) is a ball then the solutions are radially symmetric and strictly radially decreasing.
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\(p\)-Laplace equations
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monotonicity and symmetry of solutions of \(p\)-Laplace equations
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moving plane method
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