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THE VARIATIONAL FORMULATION OF THE FOKKER-PLANCK EQUATION

- R. Jordan, D. Kinderlehrer, F. Otto
- Mathematics
- 1996

The Fokker--Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It ...

THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION

- F. Otto
- Mathematics
- 31 January 2001

We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show… Expand

Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

- F. Otto, C. Villani
- Mathematics
- 1 June 2000

Abstract We show that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6 , 587–600) for the Gaussian measure, are implied by logarithmic Sobolev… Expand

An optimal variance estimate in stochastic homogenization of discrete elliptic equations

We consider a discrete elliptic equation with random coefficients $A$, which (to fix ideas) are identically distributed and independent from grid point to grid point $x\in\mathbb{Z}^d$. On scales… Expand

L1-Contraction and Uniqueness for Quasilinear Elliptic–Parabolic Equations

- F. Otto
- Mathematics
- 10 October 1996

Abstract We prove the L 1 -contraction principle and uniqueness of solutions for quasilinear elliptic–parabolic equations of the form[formula]where b is monotone nondecreasing and continuous. We… Expand

Threshold dynamics for networks with arbitrary surface tensions

We present and study a new algorithm for simulating the N-phase mean curvature motion for an arbitrary set of (isotropic) surface tensions. The departure point is the threshold dynamics algorithm of… Expand

A Regularity Theory for Random Elliptic Operators

- A. Gloria, Stefan Neukamm, F. Otto
- Mathematics
- 9 September 2014

Since the seminal results by Avellaneda & Lin it is known that elliptic operators with periodic coefficients enjoy the same regularity theory as the Laplacian on large scales. In a recent inspiring… Expand

An optimal error estimate in stochastic homogenization of discrete elliptic equations

We consider a discrete elliptic equation with random coefficients $A$, which (to fix ideas) are identically distributed and independent from grid point to grid point $x\in\mathbb{Z}^d$. On scales… Expand

Upper Bounds on Coarsening Rates

Abstract: We consider two standard models of surface-energy-driven coarsening: a constant-mobility Cahn-Hilliard equation, whose large-time behavior corresponds to Mullins-Sekerka dynamics; and a… Expand

Quantification of ergodicity in stochastic homogenization: optimal bounds via spectral gap on Glauber dynamics

- A. Gloria, Stefan Neukamm, F. Otto
- Mathematics
- 16 January 2013

We study quantitatively the effective large-scale behavior of discrete elliptic equations on the lattice $$\mathbb Z^d$$Zd with random coefficients. The theory of stochastic homogenization relates… Expand

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