Controlled viscosity solutions of fully nonlinear rough PDEs

Massimiliano Gubinelli; Samy Tindel; Iván Torrecilla

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arXiv · 1403.2832

Controlled viscosity solutions of fully nonlinear rough PDEs

Massimiliano Gubinelli·Samy Tindel·Iván Torrecilla

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Abstract

We propose a definition of viscosity solutions to fully nonlinear PDEs driven by a rough path via appropriate notions of test functions and rough jets. These objects will be defined as controlled processes with respect to the driving rough path. We show that this notion is compatible with the seminal results of Lions and Souganidis and with the recent results of Friz and coauthors on fully non-linear SPDEs with rough drivers.

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Massimiliano Gubinelli, Samy Tindel, Iván Torrecilla. 2014-03-12. Controlled viscosity solutions of fully nonlinear rough PDEs. https://arxiv.org/abs/1403.2832

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