20 Settembre, 2019 11:15

Sezione di Analisi

Decay and Sobolev regularity properties for solutions at infinity of (nonlinear) PDEs

Stefano Pigola, Università dell’Insubria

Aula seminari 3° piano

I will present some recent results on the global behaviour of nonnegative and bounded subsolutions of ${\mathrm{\Delta }}_{p}u=f(u)$ over an exterior domain of a complete Riemannian manifold. I shall discuss geometric conditions under which such a subsolution decays to zero at infinity. The main tools are represented by (a nonlinear version of) the Feller property and some global comparison results. These, in turn, are related to a new characterization of the ($p$-)stochastic completeness of the manifold in terms of the Sobolev space $W^{1,p}$.