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A remark on the definitions of viscosity solutions for the integro-differential equations with L{é}vy operators
remark definitions of viscosity solutions integro-differential equations
2011/1/21
In this note, we shall consider the following problem F(x, u,∇u,∇2u)−ZRN [u(x+z)−u(x)−1|z|<1h∇u(x).
Explicit Singular Viscosity Solutions of the Aronsson Equation
Aronsson Equation Viscosity Solutions C1 Regularity Problem
2011/2/25
We establish that when n 2 and H 2 C1(Rn) is a Hamiltonian such that some level set contains a line segment.
Large Deviations Principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections
Large Deviations Principle diffusions with oblique reflections
2011/1/21
We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control pro...
Degenerate diffusion with a drift potential: a viscosity solutions approach, joint work with I. C. Kim, truncated version
drift potential viscosity solutions approach
2010/11/23
This is a truncated version of the paper "Degenerate diffusion with a drift potential: a viscosity solutions approach", co-authored with I. C. Kim. The purpose of this version is to withdraw the claim...
A Direct Proof of the Equivalence Between the Entropy Solutions of Conservation Laws and Viscosity Solutions of Hamilton-Jacobi Equations In One-Space Variable
Hamilton-Jacobi equation Conservation law Viscosity solution Entropy solution Front tracking method
2008/7/3
A Direct Proof of the Equivalence Between the Entropy Solutions of Conservation Laws and Viscosity Solutions of Hamilton-Jacobi Equations In One-Space Variable.