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Sharp interface limit for a quasi-linear large deviation rate function

Takashi Kagaya, Kenkichi Tsunoda

Abstract

We discuss the sharp interface limit, leading to a mean curvature flow energy, for the rate function of the large deviation principle of a Glauber+Kawasaki process with speed change. We provide an explicit formula of the limiting functional given by the mobility and the transport coefficient.

Sharp interface limit for a quasi-linear large deviation rate function

Abstract

We discuss the sharp interface limit, leading to a mean curvature flow energy, for the rate function of the large deviation principle of a Glauber+Kawasaki process with speed change. We provide an explicit formula of the limiting functional given by the mobility and the transport coefficient.
Paper Structure (9 sections, 11 theorems, 175 equations)

This paper contains 9 sections, 11 theorems, 175 equations.

Table of Contents

  1. Introduction
  2. Preparations
  3. Proof of Theorem \ref{['thm2-1']}
  4. Preliminary computations
  5. Minimizing problem
  6. Proof of (1) of Theorem \ref{['thm2-1']}
  7. Proof of (2) of Theorem \ref{['thm2-1']}
  8. Analytic properties
  9. Geometric properties

Key Result

Theorem 1.1

Assume the properties (A1)--(A4) hold. Let $\Gamma=\{\Gamma_t\}_{t\in[0,T]}$ be a family of oriented smooth hyper-surfaces with $\Gamma_t=\partial\Omega_t$ for some open $\Omega_t\subset {\mathbb T}^d$ and with the finite surface area for any $t \in [0,T]$. Let also $\overline{u}$ be the unique smoo Then we have the following.

Theorems & Definitions (21)

  • Theorem 1.1
  • Lemma 2.1
  • proof
  • Proposition 2.2
  • Proposition 3.1
  • proof
  • Proposition 3.2
  • proof
  • Proposition 3.3
  • proof
  • ...and 11 more