Geodesic
Cauchy problems for noncoercive Hamilton–Jacobi–Isaacs equations with discontinuous coefficients
Cecilia De Zan1 ; Pierpaolo Soravia1
1Università di Padova, Italy
Interfaces and free boundaries, Tome 12 (2010) no. 3, pp. 347-368

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DOI

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–Carathéodory eikonal equation with discontinuous refraction index of a family of vector fields satisfying the Hörmander condition. Our results are also of interest in connection with geometric flows with discontinuous velocity in anisotropic media with a non-euclidian ambient space.
DOI : 10.4171/ifb/238
Classification : 35-XX, 49-XX, 00-XX

Cecilia De Zan  1   ; Pierpaolo Soravia  1

1 Università di Padova, Italy 
Cecilia De Zan; Pierpaolo Soravia. Cauchy problems for noncoercive Hamilton–Jacobi–Isaacs equations with discontinuous coefficients. Interfaces and free boundaries, Tome 12 (2010) no. 3, pp. 347-368. doi: 10.4171/ifb/238
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     author = {Cecilia De Zan and Pierpaolo Soravia},
     title = {Cauchy problems for noncoercive {Hamilton{\textendash}Jacobi{\textendash}Isaacs} equations with discontinuous coefficients},
     journal = {Interfaces and free boundaries},
     pages = {347--368},
     year = {2010},
     volume = {12},
     number = {3},
     doi = {10.4171/ifb/238},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/238/}
}
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