We investigate comparison and existence results for viscosity solutions of fully nonlinear,
second-order, elliptic, possibly degenerate equations. These results complement those …

The notion of viscosity solutions of scalar fully nonlinear partial differential equations of
second order provides a framework in which startling comparison and uniqueness …

There are several interesting examples of equations governing motion of hypersurfaces
bounding two phases of materials in various sciences. Such a hypersurface is called an …

In this note I discuss in some detail, but without all the occasionally cumbersome
technicalities, a general theory about propagating fronts, ie" hypersurfaces" moving with …

We prove several comparison and existence theorems for viscosity solutions of fully
nonlinear degenerate elliptic equations. One of them extends some recent uniqueness …

(1.1) F (x, u, Du) 0 in, where f is an open subset of RN (we will actually replace RN by a
Banach space in Sections 2 and 3), F: R RNR is continuous, u" fR is the unknown and Du …

The connection between the weak theories for a class of geometric equations and the
asymptotics of appropriately rescaled reaction-diffusion equations is rigorously established …

Motivated by various Hamilton–Jacobi–Bellman equations arising in deteministic optimal
control we will modify the concept of viscosity solution introduced by Crandall and Lions for …

Discontinuous solutions of deterministic optimal stopping time problems Page 1 RAIRO
MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE G. BARLES B. PERTHAME …

(O-2) the problem is to characterize the value function V”:[0, T] x IR"-+ IR', where Z [t, T] is the
class of measurable functions [:[t, T]+ ZC IRe. This problem arises in at least one important …