New regularity results for Hamilton-Jacobi equations and long time behavior of pathwise (stochastic) viscosity solutions

DOI10.1007/s40687-020-00214-7zbMath1444.60065OpenAlexW3041231746MaRDI QIDQ783087

Panagiotis E. Souganidis, Pierre-Louis Lions

Publication date: 30 July 2020

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40687-020-00214-7

zbMATH Keywords

long-time behaviorviscosity solutionsstochastic viscosity solutionsregularizing effectpathwise solutionstochastic Hamilton-Jacobi equations

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Viscosity solutions to PDEs (35D40) Hamilton-Jacobi equations (35F21)

Related Items (7)

Pathwise Solutions for Fully Nonlinear First- and Second-Order Partial Differential Equations with Multiplicative Rough Time Dependence ⋮ Differentiability With Respect to the Initial Condition for Hamilton--Jacobi Equations ⋮ Interpolation results for pathwise Hamilton-Jacobi equations ⋮ Non-equilibrium large deviations and parabolic-hyperbolic PDE with irregular drift ⋮ Long-time behavior of stochastic Hamilton-Jacobi equations ⋮ Regularizing effect for unbounded flux-limited viscosity solutions of a discontinuous Hamilton-Jacobi equation on junction ⋮ Reachable set for Hamilton-Jacobi equations with non-smooth Hamiltonian and scalar conservation laws

Cites Work

• Maximal solutions and universal bounds for some partial differential equations of evolution
• A remark on regularization in Hilbert spaces
• Regularization by noise for stochastic Hamilton-Jacobi equations
• Points of increase for random walks
• Speed of propagation for Hamilton-Jacobi equations with multiplicative rough time dependence and convex Hamiltonians
• Fully nonlinear stochastic partial differential equations
• Fully nonlinear stochastic partial differential equations: non-smooth equations and applications
• Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations
• Unnamed Item

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