We study the Cauchy problem for a homogeneous and not necessarily coercive Hamilton-Jacobi-Isaacs equation with an x-dependent, piecewise continuous coefficient. We prove that under suitable assumptions there exists a unique and continuous viscosity solution. The result applies in particular to the Carnot-Caratheodory eikonal equation with discontinuous refraction index of a family of vector fields satisfying the Hormander condition. Our results are also of interest in connection with geometric flows with discontinuous velocity in anisotropic media with a non-euclidian ambient space.

Cauchy problems for noncoercive Hamilton-Jacobi-Isaacs equations with discontinuous coefficients

DE ZAN, CECILIA;SORAVIA, PIERPAOLO
2010

Abstract

We study the Cauchy problem for a homogeneous and not necessarily coercive Hamilton-Jacobi-Isaacs equation with an x-dependent, piecewise continuous coefficient. We prove that under suitable assumptions there exists a unique and continuous viscosity solution. The result applies in particular to the Carnot-Caratheodory eikonal equation with discontinuous refraction index of a family of vector fields satisfying the Hormander condition. Our results are also of interest in connection with geometric flows with discontinuous velocity in anisotropic media with a non-euclidian ambient space.
File in questo prodotto:
File Dimensione Formato  
IFB 2010-12-03-04.pdf

accesso aperto

Tipologia: Published (publisher's version)
Licenza: Accesso libero
Dimensione 231.34 kB
Formato Adobe PDF
231.34 kB Adobe PDF Visualizza/Apri
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/11577/2428048
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 10
social impact