Developing an original idea of De Giorgi, we introduce a new and purely variational approach to the Cauchy Problem for a wide class of defocusing hyperbolic equations. The main novel feature is that the solu- tions are obtained as limits of functions that minimize suitable functionals in space{time (where the initial data of the Cauchy Problem serve as pre- scribed boundary conditions). This opens up the way to new connections between the hyperbolic world and that of the Calculus of Variations. Also dissipative equations can be treated. Finally, we discuss several examples of equations that t in this framework, including nonlocal equations, in particular equations with the fractional Laplacian.

A minimization approach to hyperbolic Cauchy problems / Serra, Enrico; Tilli, Paolo. - In: JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY. - ISSN 1435-9855. - STAMPA. - 18:9(2016), pp. 2019-2044. [10.4171/JEMS/637]

A minimization approach to hyperbolic Cauchy problems

SERRA, Enrico;TILLI, PAOLO
2016

Abstract

Developing an original idea of De Giorgi, we introduce a new and purely variational approach to the Cauchy Problem for a wide class of defocusing hyperbolic equations. The main novel feature is that the solu- tions are obtained as limits of functions that minimize suitable functionals in space{time (where the initial data of the Cauchy Problem serve as pre- scribed boundary conditions). This opens up the way to new connections between the hyperbolic world and that of the Calculus of Variations. Also dissipative equations can be treated. Finally, we discuss several examples of equations that t in this framework, including nonlocal equations, in particular equations with the fractional Laplacian.
File in questo prodotto:
File Dimensione Formato  
jems_serra-tilli.pdf

non disponibili

Tipologia: 2. Post-print / Author's Accepted Manuscript
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 211.79 kB
Formato Adobe PDF
211.79 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
edit..pdf

non disponibili

Descrizione: articolo principale
Tipologia: 2a Post-print versione editoriale / Version of Record
Licenza: Non Pubblico - Accesso privato/ristretto
Dimensione 5.8 MB
Formato Adobe PDF
5.8 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

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/11583/2651082