Dimensionality of Local Minimizers of the Interaction Energy

D. Balagué Guardia; Jose Antonio Carrillo; Thomas Laurent; Gael Raoul

doi:10.1007/s00205-013-0644-6

Dimensionality of Local Minimizers of the Interaction Energy

D. Balagué Guardia, Jose Antonio Carrillo, Thomas Laurent, Gael Raoul

Research output: Contribution to journal › Article › Scientific › peer-review

Abstract

In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated with a repulsive–attractive potential. We show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.

Original language	English
Pages (from-to)	1055–1088
Journal	Archive for Rational Mechanics and Analysis
Volume	209
Issue number	3
DOIs	https://doi.org/10.1007/s00205-013-0644-6
Publication status	Published - 2013
Externally published	Yes

Keywords

Local Minimizer
Interaction Energy
Hausdorff dimension
Borel Probability Measure
Attractive Potential

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10.1007/s00205-013-0644-6

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@article{e4d96577b153433ab6cf7b6d210be37e,

title = "Dimensionality of Local Minimizers of the Interaction Energy",

abstract = "In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated with a repulsive–attractive potential. We show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.",

keywords = "Local Minimizer, Interaction Energy, Hausdorff dimension, Borel Probability Measure, Attractive Potential",

author = "{Balagu{\'e} Guardia}, D. and Carrillo, {Jose Antonio} and Thomas Laurent and Gael Raoul",

year = "2013",

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language = "English",

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T1 - Dimensionality of Local Minimizers of the Interaction Energy

AU - Balagué Guardia, D.

AU - Carrillo, Jose Antonio

AU - Laurent, Thomas

AU - Raoul, Gael

PY - 2013

Y1 - 2013

N2 - In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated with a repulsive–attractive potential. We show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.

AB - In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated with a repulsive–attractive potential. We show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.

KW - Local Minimizer

KW - Interaction Energy

KW - Hausdorff dimension

KW - Borel Probability Measure

KW - Attractive Potential

U2 - 10.1007/s00205-013-0644-6

DO - 10.1007/s00205-013-0644-6

M3 - Article

SN - 0003-9527

VL - 209

SP - 1055

EP - 1088

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 3

ER -

Dimensionality of Local Minimizers of the Interaction Energy

Abstract

Keywords

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