We overview some L p -extensions of the classical divergence theorem to non-compact Riemannian manifolds without boundary. The red wire connecting all these extensions is represented by the notion of parabolicity with respect to the p-Laplace operator. It is a non-linear differential operator which is naturally related to the p-energy of maps and, therefore, to L p -integrability properties of vector fields. To show the usefulness of these tools, a certain number of applications both to (systems of) PDEs and to the global geometry of the underlying manifold are presented. These lecture notes contain, in a slightly expanded form, the material presented at the Summer School in Di erential Geometry held in January 2012 in the Universidade Federal do Ceara-UFC, Fortaleza. The course aims at giving an overview of some Lp-extensions of the classical divergence theorem to non-compact Riemannian manifolds without boundary.

Global divergence theorems in nonlinear PDEs and geometry

PIGOLA, STEFANO;SETTI, ALBERTO GIULIO
2014-01-01

Abstract

We overview some L p -extensions of the classical divergence theorem to non-compact Riemannian manifolds without boundary. The red wire connecting all these extensions is represented by the notion of parabolicity with respect to the p-Laplace operator. It is a non-linear differential operator which is naturally related to the p-energy of maps and, therefore, to L p -integrability properties of vector fields. To show the usefulness of these tools, a certain number of applications both to (systems of) PDEs and to the global geometry of the underlying manifold are presented. These lecture notes contain, in a slightly expanded form, the material presented at the Summer School in Di erential Geometry held in January 2012 in the Universidade Federal do Ceara-UFC, Fortaleza. The course aims at giving an overview of some Lp-extensions of the classical divergence theorem to non-compact Riemannian manifolds without boundary.
http://www.emis.de/journals/em/images/pdf/em_26.pdf
Divergence theorem; p-Laplacian; p-parabolicity
Pigola, Stefano; Setti, ALBERTO GIULIO
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2019044
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact