Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems. (English) Zbl 0665.35025
The author studies concavity properties of the solution to
\[
\Delta_ pu=| u|^{p-2} u\quad in\quad \Omega,\quad u\geq 0,\quad or\quad \Delta_ pu=1\quad in\quad \Omega
\]
(where \(\Delta_ p\) is the nonlinear degenerate p-Laplacian and the Poincaré constant of \(W_ 0^{1,p}(\Omega))\) with zero Dirichlet boundary condition.
Reviewer: M.Biroli
MSC:
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35E10 | Convexity properties of solutions to PDEs with constant coefficients |
| 35J70 | Degenerate elliptic equations |
Keywords:
concavity; nonlinear degenerate p-Laplacian; Poincaré constant; zero Dirichlet boundary conditionReferences:
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