论文信息 - Eikonal equations and pathwise solutions to fully non-linear SPDEs

Eikonal equations and pathwise solutions to fully non-linear SPDEs

We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend the class of equations studied so far by the last two authors.

[1] G. Barles. Solutions de viscosité des équations de Hamilton-Jacobi , 1994 .

[2] Luciano Tubaro,et al. Fully nonlinear stochastic partial differential equations , 1996 .

[3] P. Souganidis,et al. Fully nonlinear stochastic partial differential equations: non-smooth equations and applications , 1998 .

[4] P. Lions,et al. User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[5] P. Souganidis,et al. Viscosity Solutions of Fully Nonlinear Stochastic Partial Differential Equatios (微分方程式の粘性解とその周辺研究集会報告集) , 2002 .

[6] Perron's method for stochastic viscosity solutions , 2016 .

[7] A. Mennucci,et al. Hamilton—Jacobi Equations and Distance Functions on Riemannian Manifolds , 2002, math/0201296.

[8] Panagiotis E. Souganidis,et al. Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations , 2000 .

[9] Panagiotis E. Souganidis,et al. Fully nonlinear stochastic PDE with semilinear stochastic dependence , 2000 .