Carlo Nitsch

A sharp isoperimetric inequiality in the plane

We show that among all the convex bounded domains in R2 having a fixed Fraenkel asymmetry index, there exists only one convex set (up to similarity) which minimizes the isoperimetric deficit. We also show how to construct this set. The result can be read as a sharp improvement of the isoperimetric inequality for convex planar domains.

A system of degenerate parabolic nonlinear PDE's: a new free boundary problem

MICHIEL BERTSCH† Istituto per le Applicazioni del Calcolo “Mauro Picone”, Consiglio Nazionale delle Ricerche, Viale del Policlinico, 137, I-00161 Roma, Italy Dipartimento di Matematica, Universita degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Roma, Italy ROBERTA DAL PASSO‡ AND CARLO NITSCH§ Dipartimento di Matematica, Universita degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica, I-00133 Roma, Italy

On Pólya's inequality for torsional rigidity and first Dirichlet eigenvalue

Let

The Neumann eigenvalue problem for the

\Omega

-Laplacian

Ω be an open set in Euclidean space with finite Lebesgue measure

The classical overdetermined Serrin problem

\vert \Omega \vert