PDE Real Analysis Seminar

Seminar information archive ~03/27Next seminarFuture seminars 03/28~

Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

2012/11/21

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Giovanni Pisante (Seconda Università degli Studi di Napoli)
Shape Optimization And Asymptotic For The Twisted Dirichlet Eigenvalue (ENGLISH)
[ Abstract ]
Aim of the talk is to discuss some recent results obtained with G. Croce and A. Henrot on a generalization of the functional defining the first twisted eigenvalue.
We look at the set functional defined by minimizing a Rayleigh quotient involving Lebesgue norms with different exponents p and q among functions satisfying a zero boundary condition as well as a zero mean condition of order q.
First under suitable conditions on p and q, that ensure the existence of a minimizing function, we investigate the validity of an isoperimetric type inequality of the Reyleigh-Faber-Krahn type.
Then we study the limit of the functional for p and q tending to 1 and to infinity and discuss the relation with the limits of the second eigenvalues of the p-laplacian operator.