Calculus of Variations and Geometric Measure Theory

On the first nontrivial Neumann eigenvalue of the infinity Laplacian

Carlo Nitsch (Dip. Mat. Univ. Napoli Federico II)

created by gelli on 09 Nov 2015
modified on 11 Nov 2015

9 dec 2015 -- 17:00   [open in google calendar]

Aula Seminari Dipartimento di Matematica di Pisa


The first nontrivial eigenfunction of the Neumann eigenvalue problem for the p-Laplacian converges, as $p$ goes to $\infty$, to a viscosity solution of a suitable eigenvalue problem for the $\infty$-Laplacian. We show among other things that the limiting eigenvalue is in fact the first nonzero eigenvalue, and derive a number consequences, which are nonlinear analogues of well-known inequalities for the linear (2-)Laplacian.