Benjamin J. Fehrman

A Liouville theorem for elliptic systems with degenerate ergodic coefficients

We study the behavior of second-order degenerate elliptic systems in divergence form with random coefficients which are stationary and ergodic. Assuming moment bounds like Chiarini and Deuschel [Arxiv preprint 1410.4483, 2014] on the coefficient field

Stochastic Homogenization of Monotone Systems of Viscous Hamilton--Jacobi Equations with Convex Nonlinearities

a

Stochastic Homogenization of Linear Elliptic Equations: Higher-Order Error Estimates in Weak Norms Via Second-Order Correctors

and its inverse, we prove an intrinsic large-scale

Exit Laws of Isotropic Diffusions in Random Environment from Large Domains

C^{1,\alpha}

Moduli Spaces of Punctured Poincaré Disks

-regularity estimate for

On The Dimension of The Virtually Cyclic Classifying Space of a Crystallographic Group

a

On the existence of an invariant measure for isotropic diffusions in random environment

-harmonic functions and obtain a first-order Liouville theorem for subquadratic

A Partial Homogenization Result for Nonconvex Viscous Hamilton-Jacobi Equations

a

A Liouville Property for Isotropic Diffusions in Random Environment

-harmonic functions.

A Liouville theorem for stationary and ergodic ensembles of parabolic systems

We consider the homogenization of monotone systems of viscous Hamilton--Jacobi equations with convex nonlinearities set in the stationary, ergodic setting. The primary focus of this paper is on collapsing systems which, as the microscopic scale tends to zero, average to a deterministic scalar Hamilton--Jacobi equation. However, our methods also apply to systems which do not collapse and, as the microscopic scale tends to zero, average to a deterministic system of Hamilton--Jacobi equations.