Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies
We obtain a sharp quantitative isoperimetric inequality for nonlocal s -perimeters, uniform with respect to s bounded away from 0. This allows us to address local and global minimality properties of balls with respect to the volume-constrained minimization of a free energy consisting of a nonlocal s...
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| Veröffentlicht in: | Communications in mathematical physics 2015-05, Vol.336 (1), p.441-507 |
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| creator | Figalli, A. Fusco, N. Maggi, F. Millot, V. Morini, M. |
| description | We obtain a sharp quantitative isoperimetric inequality for nonlocal
s
-perimeters, uniform with respect to
s
bounded away from 0. This allows us to address local and global minimality properties of balls with respect to the volume-constrained minimization of a free energy consisting of a nonlocal
s
-perimeter plus a non-local repulsive interaction term. In the particular case
s
= 1, the
s
-perimeter coincides with the classical perimeter, and our results improve the ones of Knuepfer and Muratov (Comm. Pure Appl. Math. 66(7):1129–1162,
2013
; Comm. Pure Appl. Math.,
2014
) concerning minimality of balls of small volume in isoperimetric problems with a competition between perimeter and a nonlocal potential term. More precisely, their result is extended to its maximal range of validity concerning the type of nonlocal potentials considered, and is also generalized to the case where local perimeters are replaced by their nonlocal counterparts. |
| doi_str_mv | 10.1007/s00220-014-2244-1 |
| format | Article |
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s
-perimeters, uniform with respect to
s
bounded away from 0. This allows us to address local and global minimality properties of balls with respect to the volume-constrained minimization of a free energy consisting of a nonlocal
s
-perimeter plus a non-local repulsive interaction term. In the particular case
s
= 1, the
s
-perimeter coincides with the classical perimeter, and our results improve the ones of Knuepfer and Muratov (Comm. Pure Appl. Math. 66(7):1129–1162,
2013
; Comm. Pure Appl. Math.,
2014
) concerning minimality of balls of small volume in isoperimetric problems with a competition between perimeter and a nonlocal potential term. More precisely, their result is extended to its maximal range of validity concerning the type of nonlocal potentials considered, and is also generalized to the case where local perimeters are replaced by their nonlocal counterparts.</description><identifier>ISSN: 0010-3616</identifier><identifier>EISSN: 1432-0916</identifier><identifier>DOI: 10.1007/s00220-014-2244-1</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis of PDEs ; Classical and Quantum Gravitation ; Complex Systems ; Mathematical and Computational Physics ; Mathematical Physics ; Mathematics ; Physics ; Physics and Astronomy ; Quantum Physics ; Relativity Theory ; Theoretical</subject><ispartof>Communications in mathematical physics, 2015-05, Vol.336 (1), p.441-507</ispartof><rights>Springer-Verlag Berlin Heidelberg 2014</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c398t-6f4108240cc2ecfcc9c06f0d41c6ba5b3cc0ab333a2a35fea7b39964c37ad5093</citedby><cites>FETCH-LOGICAL-c398t-6f4108240cc2ecfcc9c06f0d41c6ba5b3cc0ab333a2a35fea7b39964c37ad5093</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00220-014-2244-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00220-014-2244-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttps://hal.sorbonne-universite.fr/hal-00955169$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Figalli, A.</creatorcontrib><creatorcontrib>Fusco, N.</creatorcontrib><creatorcontrib>Maggi, F.</creatorcontrib><creatorcontrib>Millot, V.</creatorcontrib><creatorcontrib>Morini, M.</creatorcontrib><title>Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies</title><title>Communications in mathematical physics</title><addtitle>Commun. Math. Phys</addtitle><description>We obtain a sharp quantitative isoperimetric inequality for nonlocal
s
-perimeters, uniform with respect to
s
bounded away from 0. This allows us to address local and global minimality properties of balls with respect to the volume-constrained minimization of a free energy consisting of a nonlocal
s
-perimeter plus a non-local repulsive interaction term. In the particular case
s
= 1, the
s
-perimeter coincides with the classical perimeter, and our results improve the ones of Knuepfer and Muratov (Comm. Pure Appl. Math. 66(7):1129–1162,
2013
; Comm. Pure Appl. Math.,
2014
) concerning minimality of balls of small volume in isoperimetric problems with a competition between perimeter and a nonlocal potential term. More precisely, their result is extended to its maximal range of validity concerning the type of nonlocal potentials considered, and is also generalized to the case where local perimeters are replaced by their nonlocal counterparts.</description><subject>Analysis of PDEs</subject><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKs_wFuuHqKTj02bYy3VFhYtfpxDNk3aLeumJFHpv3eXFY-eBmaeZ-B9EbqmcEsBJncJgDEgQAVhTAhCT9CICs4IKCpP0QiAAuGSynN0kdIeABSTcoTWqxQOLtYfLscjNu0Gv2ZT1U2dj3gd-1OuXcLB43vTNAl_13mHX1w6OJtxDvgptE2wpsGL1sVth16iM2-a5K5-5xi9Pyze5ktSPj-u5rOSWK6mmUgvKEyZAGuZs95aZUF62AhqZWWKilsLpuKcG2Z44Z2ZVFwpKSyfmE0Bio_RzfB3Zxp96AKYeNTB1Ho5K3W_6xIWBZXqi3YsHVgbQ0rR-T-Bgu7r00N9uqtP9_Xp3mGDkzq23bqo9-Eztl2kf6Qf70NynA</recordid><startdate>20150501</startdate><enddate>20150501</enddate><creator>Figalli, A.</creator><creator>Fusco, N.</creator><creator>Maggi, F.</creator><creator>Millot, V.</creator><creator>Morini, M.</creator><general>Springer Berlin Heidelberg</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>20150501</creationdate><title>Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies</title><author>Figalli, A. ; Fusco, N. ; Maggi, F. ; Millot, V. ; Morini, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c398t-6f4108240cc2ecfcc9c06f0d41c6ba5b3cc0ab333a2a35fea7b39964c37ad5093</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Analysis of PDEs</topic><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Mathematics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Figalli, A.</creatorcontrib><creatorcontrib>Fusco, N.</creatorcontrib><creatorcontrib>Maggi, F.</creatorcontrib><creatorcontrib>Millot, V.</creatorcontrib><creatorcontrib>Morini, M.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Figalli, A.</au><au>Fusco, N.</au><au>Maggi, F.</au><au>Millot, V.</au><au>Morini, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. Math. Phys</stitle><date>2015-05-01</date><risdate>2015</risdate><volume>336</volume><issue>1</issue><spage>441</spage><epage>507</epage><pages>441-507</pages><issn>0010-3616</issn><eissn>1432-0916</eissn><abstract>We obtain a sharp quantitative isoperimetric inequality for nonlocal
s
-perimeters, uniform with respect to
s
bounded away from 0. This allows us to address local and global minimality properties of balls with respect to the volume-constrained minimization of a free energy consisting of a nonlocal
s
-perimeter plus a non-local repulsive interaction term. In the particular case
s
= 1, the
s
-perimeter coincides with the classical perimeter, and our results improve the ones of Knuepfer and Muratov (Comm. Pure Appl. Math. 66(7):1129–1162,
2013
; Comm. Pure Appl. Math.,
2014
) concerning minimality of balls of small volume in isoperimetric problems with a competition between perimeter and a nonlocal potential term. More precisely, their result is extended to its maximal range of validity concerning the type of nonlocal potentials considered, and is also generalized to the case where local perimeters are replaced by their nonlocal counterparts.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00220-014-2244-1</doi><tpages>67</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Analysis of PDEs Classical and Quantum Gravitation Complex Systems Mathematical and Computational Physics Mathematical Physics Mathematics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical |
| title | Isoperimetry and Stability Properties of Balls with Respect to Nonlocal Energies |
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