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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
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