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An Ohta-Kawasaki Model set on the space

Lorena Aguirre Salazar, Xin Yang Lu, Jun-cheng Wei

Abstract

We examine a non-local diffuse interface energy with Coulomb repulsion in three dimensions inspired by the Thomas-Fermi-Dirac-von Weizsäcker, and the Ohta-Kawasaki models. We consider the corresponding mass-constrained variational problem and show the existence of minimizers for small masses, and the absence of minimizers for large masses.

An Ohta-Kawasaki Model set on the space

Abstract

We examine a non-local diffuse interface energy with Coulomb repulsion in three dimensions inspired by the Thomas-Fermi-Dirac-von Weizsäcker, and the Ohta-Kawasaki models. We consider the corresponding mass-constrained variational problem and show the existence of minimizers for small masses, and the absence of minimizers for large masses.
Paper Structure (4 sections, 12 theorems, 58 equations)

This paper contains 4 sections, 12 theorems, 58 equations.

Table of Contents

  1. Introduction
  2. General Estimates
  3. Proof of part (a) of Theorem \ref{['Th1']}
  4. Proof of part (b) of Theorem \ref{['Th1']}

Key Result

Theorem 1.1

There exist constants $0<\mathcal{Z}\leq M_1\leq M_2<\infty$ such that:

Theorems & Definitions (27)

  • Theorem 1.1
  • Remark 1.2
  • Lemma 2.1
  • proof
  • Corollary 2.2
  • proof
  • Lemma 2.3
  • proof
  • Corollary 2.4
  • proof
  • ...and 17 more