Large Volume Minimizers of a Nonlocal Isoperimetric Problem: Theoretical and Numerical Approaches

DOI10.1137/17M1139400WikidataQ129603569 ScholiaQ129603569MaRDI QIDQ4570974

François Générau, Edouard Oudet

Publication date: 5 July 2018

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.06028

zbMATH Keywords

calculus of variationsgamma-convergenceRiesz potentialnonlocal isoperimetric problem

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Optimization of shapes other than minimal surfaces (49Q10) Numerical methods for variational inequalities and related problems (65K15)

Related Items (5)

Nonexistence of minimizers for a nonlocal perimeter with a Riesz and a background potential ⋮ Bifurcation and fission in the liquid drop model: A phase-field approach ⋮ A nonlocal isoperimetric problem with density perimeter ⋮ Large mass minimizers for isoperimetric problems with integrable nonlocal potentials ⋮ Large mass rigidity for a liquid drop model in 2D with kernels of finite moments

Uses Software

• Ipopt

Cites Work

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• Nonexistence of large nuclei in the liquid drop model
• Isoperimetry and stability properties of balls with respect to nonlocal energies
• On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
• On an Isoperimetric Problem with a Competing Nonlocal Term I: The Planar Case
• Nonexistence of a Minimizer for Thomas-Fermi-Dirac-von Weizsäcker Model
• Local and Global Minimality Results for a Nonlocal Isoperimetric Problem on $\mathbb{R}^N$
• Small Volume-Fraction Limit of the Diblock Copolymer Problem: II. Diffuse-Interface Functional
• Ground-states for the liquid drop and TFDW models with long-range attraction

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