Large mass minimizers for isoperimetric problems with integrable nonlocal potentials

M Pegon - Nonlinear Analysis, 2021 - Elsevier
This paper is concerned with volume-constrained minimization problems derived from
Gamow's liquid drop model for the atomic nucleus, involving the competition of a perimeter …

Droplet breakup in the liquid drop model with background potential

S Alama, L Bronsard, R Choksi… - Communications in …, 2019 - World Scientific
We consider a variant of Gamow's liquid drop model, with a general repulsive Riesz kernel
and a long-range attractive background potential with weight Z. The addition of the …

Large mass rigidity for a liquid drop model in D with kernels of finite moments

B Merlet, M Pegon - Journal de l'Ecole polytechnique—Mathématiques, 2022 - numdam.org
Motivated by Gamow's liquid drop model in the large mass regime, we consider an
isoperimetric problem in which the standard perimeter P (E) is replaced by P (E)-γPε (E) …

Large volume minimizers of a nonlocal isoperimetric problem: theoretical and numerical approaches

F Générau, E Oudet - SIAM Journal on Mathematical Analysis, 2018 - SIAM
We consider the volume-constrained minimization of the sum of the perimeter and the Riesz
potential. We add an external potential of the form ‖x‖^β that provides the existence of a …

Ground states for a nonlocal isoperimetric problem with two interacting phases

G Zhang, S Huang - Applicable Analysis, 2024 - Taylor & Francis
ABSTRACT A nonlocal isoperimetric problem of two interacting phases with power-law
potentials is investigated. Using the concentration-compactness lemma for sets of finite …

[HTML][HTML] 两个相位的非局部等周问题的基态解的存在性

黄帅飞 - Advances in Applied Mathematics, 2022 - hanspub.org
本文主要研究了具有幂律势的两个相位的非局部等周问题. 利用集中紧性原理,
证明了具有两个相位的非局部等周问题基态解的存在性. 本文是在泛函的极小值的存在性的背景 …

Mass splitting in the Thomas–Fermi–Dirac–von Weizsäcker model with background potential

L Aguirre Salazar, S Alama, L Bronsard - Journal of Mathematical …, 2020 - pubs.aip.org
We consider minimization problems of the Thomas–Fermi–Dirac–von Weizsäcker (TFDW)
type in which the Newtonian potential is perturbed by a background potential satisfying mild …

[HTML][HTML] On an isoperimetric problem with power-law potentials and external attraction

G Zhang, X Geng - Journal of Mathematical Analysis and Applications, 2020 - Elsevier
In this paper, an isoperimetric problem with power-law potentials and external attraction is
considered. Using concentration-compactness lemma for sets of finite perimeter which was …

The block copolymer and its related problems and mathematical models

C Zhang - 2024 - knowledgecommons.lakeheadu.ca
By competing short and long-range interactions, there exists some energies have been
introduced and studied in the mathematics. These energies are relevance to the diblock …

On a stable variational approximation of the cut locus, and a non-local isoperimetric problem

F Générau - 2020 - theses.hal.science
This thesis is composed of two parts. In the first part, we study a generalization of the
variational problem of elastic-plastic torsion problem to manifolds. We show that in the case …