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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