Eikonal equations and pathwise solutions to fully non-linear SPDEs
Tóm tắt
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.
Tài liệu tham khảo
Barles, G.: Solutions de Viscosité des Équations de Hamilton-Jacobi. Springer, Paris (2004)
Crandall, M., Ishii, H., Lions, P.-L.: User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. 27, 1–67 (1992)
Diehl, J., Friz, P., Oberhauser, H.: Regularity theory for RPDEs and parabolic comparison revisited. In: Crisan, D. (ed.) Stochastic Analysis and Applications, Springer Proceedings in Mathematics & Statistics, vol. 100 (2014)
Lions, P.-L., Souganidis, P.E.: Viscosity solutions of fully nonlinear stochastic partial differential equations. Sūrikaisekikenkyūsho Kōkyūroku (1287), 58–65 (2002). Viscosity solutions of differential equations and related topics (Japanese) (Kyoto, 2001)
Lions, P.-L., Souganidis, P.E.: Fully nonlinear stochastic partial differential equations. C. R. Acad. Sci. Paris Sér. I Math. 326(9), 1085–1092 (1998)
Lions, P.-L., Souganidis, P.E.: Fully nonlinear stochastic partial differential equations: non-smooth equations and applications. C. R. Acad. Sci. Paris Sér. I Math. 327(8), 735–741 (1998)
Lions, P.-L., Souganidis, P.E.: Fully nonlinear stochastic pde with semilinear stochastic dependence. C. R. Acad. Sci. Paris Sér. I Math. 331(8), 617–624 (2000)
Lions, P.-L., Souganidis, P.E.: Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations. C. R. Acad. Sci. Paris Sér. I Math. 331(10), 783–790 (2000)
Lions, P.-L., Souganidis, P.E.: Stochastic viscosity solutions. Book (in preparation)
Lions, P.-L., Souganidis, P.E.: Stochastic viscosity solutions of spatially dependent Hamilton-Jacobi equations with multiple paths (in preparation)
Lions, P.-L., Souganidis, P.E.: (in preparation)
Mantegazza, C., Mennucci, A.C.: Hamilton-Jacobi equations and distance functions on Riemannian manifolds. Appl. Math. Optim. 47(1) (2002)
Seeger, B.: Perron’s method for stochastic viscosity solutions. Preprint, arXiv:1605.01108