Stochastic and partial differential equations on non-smooth time-dependent domains
| Autor: | Niklas L.P. Lundström, Thomas Önskog |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Partial differential equation 35D05 49L25 35D05 49L25 60J50 60J60 Applied Mathematics 010102 general mathematics Mathematical analysis 01 natural sciences Parabolic partial differential equation 010104 statistics & probability Stochastic differential equation Nonlinear system Mathematics - Analysis of PDEs Modeling and Simulation FOS: Mathematics Boundary value problem Uniqueness 0101 mathematics Viscosity solution Mathematics Oblique reflection Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.1503.05433 |
| Popis: | In this article, we consider non-smooth time-dependent domains whose boundary is W 1 , p in time and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic differential equations with oblique reflection. Secondly, we prove, using the theory of viscosity solutions, a comparison principle for fully nonlinear second-order parabolic partial differential equations with oblique derivative boundary conditions. As a consequence, we obtain uniqueness, and, by barrier construction and Perron’s method, we also conclude existence of viscosity solutions. Our results generalize two articles by Dupuis and Ishii to time-dependent domains. |
| Databáze: | OpenAIRE |
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