Geodesic
Integral formulations of the geometric eikonal equation
Aurélien Monteillet1
1Université de Bretagne Occidentale, Brest, France
Interfaces and free boundaries, Tome 9 (2007) no. 2, pp. 253-283

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DOI

We prove integral formulations of the eikonal equation ut​=c(x,t)∣Du∣, equivalent to the notion of viscosity solution in the framework of the set-theoretic approach to front propagation problems. We apply these integral formulations to investigate the regularity of the front: we prove that under regularity assumptions on the velocity c, the front has locally finite perimeter in {c=0}, and we give a time-integral estimate of its perimeter.
DOI : 10.4171/ifb/164
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Eikonal equation, viscosity solutions, set-theoretic approach, functions of bounded variation and sets of finite perimeter

Aurélien Monteillet  1

1 Université de Bretagne Occidentale, Brest, France 
Aurélien Monteillet. Integral formulations of the geometric eikonal equation. Interfaces and free boundaries, Tome 9 (2007) no. 2, pp. 253-283. doi: 10.4171/ifb/164
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     title = {Integral formulations of the geometric eikonal equation},
     journal = {Interfaces and free boundaries},
     pages = {253--283},
     year = {2007},
     volume = {9},
     number = {2},
     doi = {10.4171/ifb/164},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/164/}
}
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