A level set crystalline mean curvature flow of surfaces [PDF]
, 2016 We introduce a new notion of viscosity solutions for the level set formulation of the motion by crystalline mean curvature in three dimensions. The solutions satisfy the comparison principle, stability with respect to an approximation by regularized ...
Giga, Yoshikazu, Požár, Norbert
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Anisotropic total variation flow of non-divergence type on a higher dimensional torus [PDF]
, 2013 We extend the theory of viscosity solutions to a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of an arbitrary dimension with diffusion given by an anisotropic total variation energy. We give a proof of a
Giga, Mi-Ho +2 more
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Lipschitz regularity results for nonlinear strictly elliptic equations and applications
, 2016 Most of lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance).
Ley, Olivier, Nguyen, Vinh Duc
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Lipschitz regularity for integro-differential equations with coercive hamiltonians and application to large time behavior [PDF]
, 2016 In this paper, we provide suitable adaptations of the "weak version of Bernstein method" introduced by the first author in 1991, in order to obtain Lipschitz regularity results and Lipschitz estimates for nonlinear integro-differential elliptic and ...
Barles, Guy, Ley, Olivier, Topp, Erwin
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Nonlinear diffusion in transparent media: the resolvent equation
, 2017 We consider the partial differential equation $$ u-f={\rm div}\left(u^m\frac{\nabla u}{|\nabla u|}\right) $$ with $f$ nonnegative and bounded and $m\in\mathbb{R}$.
Giacomelli, Lorenzo +2 more
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Viscosity solutions of general viscous Hamilton-Jacobi equations
, 2014 We present comparison principles, Lipschitz estimates and study state constraints problems for degenerate, second-order Hamilton-Jacobi equations.Comment: 35 pages, minor ...
Armstrong, Scott N., Tran, Hung V.
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Regularity Results and Large Time Behavior for Integro-Differential Equations with Coercive Hamiltonians [PDF]
, 2014 In this paper we obtain regularity results for elliptic integro-differential equations driven by the stronger effect of coercive gradient terms. This feature allows us to construct suitable strict supersolutions from which we conclude H\"older estimates ...
Barles, Guy +3 more
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The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions [PDF]
, 2016 We discuss existence, uniqueness, regularity and boundary behaviour of solutions of the Dirichlet problem for the prescribed anisotropic mean curvature equation \begin{equation*} {\rm -div}\left({\nabla u}/{\sqrt{1 + |\nabla u|^2}}\right) = -au ...
Corsato, Chiara +2 more
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On viscosity solutions to the Dirichlet problem for elliptic branches of inhomogeneous fully nonlinear equations [PDF]
, 2017 For scalar fully nonlinear partial differential equations F(x, D2u(x)) = 0 with x ∈ Ω b RN , we present a general theory for obtaining comparison principles and well posedness for the associated Dirichlet problem, where F(x, ·) need not be monotone on ...
Cirant, Marco, Payne, Kevin R.
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Irreversible Games with Incomplete Information: The Asymptotic Value [PDF]
, 2010 Irreversible games are stochastic games in which once the play leaves a state it never revisits that state. This class includes absorbing games. This paper proves the existence and a characterization of the asymptotic value for any finite irreversible ...
Laraki, Rida
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