Integral formulations of the geometric eikonal equation | Zendy

Aurélien Monteillet | Zendy

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Integral formulations of the geometric eikonal equation

Author(s) -

Aurélien Monteillet

Publication year - 2007

Publication title -

interfaces and free boundaries mathematical analysis computation and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.964

H-Index - 39

eISSN - 1463-9971

pISSN - 1463-9963

DOI - 10.4171/ifb/164

Subject(s) - eikonal equation , perimeter , viscosity solution , eikonal approximation , mathematics , integral equation , front (military) , mathematical analysis , viscosity , set (abstract data type) , mathematical physics , geometry , physics , computer science , quantum mechanics , meteorology , programming language

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 6= 0}, and we give a time-integral estimate of its perimeter.

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