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

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SRQW03 - Scaling limits & SPDEs: recent developments and future directions

I will discuss two new regularity results (regularizing effect and propagation of regularity) for viscosity solutions of uniformly convex Hamilton-Jacobi equations. In turn, the new estimates yield new intermittent stochastic regularization for pathwise (stochastic) viscosity solutions of Hamilton-Jacobi equations with uniformly convex Hamiltonians and rough multiplicative time dependence. The intermittent regularity estimates are then used to study the long time behavior of the pathwise (stochastic) viscosity solutions of convex Hamilton-Jacobi equations. This is joint work with P. L. Lions.

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