Barbara Brandolini

Sharp Estimates for Eigenfunctions of a Neumann Problem

In this paper we provide some bounds for eigenfunctions of the Laplacian with homogeneous Neumann boundary conditions in a bounded domain Ω of ℝ n . To this aim we use the so-called symmetrization techniques and the obtained estimates are asymptotically sharp, at least in the bidimensional case, when the isoperimetric constant relative to Ω goes to 0.

Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems

In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ 1 ( Ω ) for the p -Laplace operator ( p > 1) in a Lipschitz bounded domain Ω in ℝ n . Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω . In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne—Weinberger inequality.

The equality case in a Poincaré–Wirtinger type inequality

In this paper, generalizing to the non smooth case already existing results, we prove that, for any convex planar set

A sharp estimate of the extinction time for the mean curvature flow

\Omega

Perimeter Symmetrization of Some Dynamic and Stationary Equations Involving the Monge-Ampère Operator

, the first non-trivial Neumann eigenvalue

Serrin-Type Overdetermined Problems: an Alternative Proof

\mu_1(\Omega)

On the stability of the Serrin problem

of the Hermite operator is greater than or equal to 1. Furthermore, and this is our main result, under some additional assumptions on

New isoperimetric estimates for solutions to Monge–Ampère equations

\Omega

A symmetrization result for Monge–Ampère type equations

, we show that

Hardy type inequalities and Gaussian measure

\mu_1(\Omega)=1