全非线性SPDEs的Eikonal方程和路径解。

Stochastic partial differential equations : analysis and computations Pub Date : 2017-01-01 Epub Date: 2016-12-03 DOI:10.1007/s40072-016-0087-9

Peter K Friz, Paul Gassiat, Pierre-Louis Lions, Panagiotis E Souganidis

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引用次数: 27

摘要

研究了黎曼几何中具有二次哈密顿算子的全非线性、可能退化的二阶随机偏微分方程的随机黏性解的存在唯一性。这些结果是新的，并且扩展了前两位作者迄今为止所研究的一类方程。

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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.

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Stochastic partial differential equations : analysis and computations

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