Regularity for non-local almost minimal boundaries and applications
We introduce a notion of non-local almost minimal boundaries similar to that introduced by Almgren in geometric measure theory. Extending methods developed recently for non-local minimal surfaces we prove that flat non-local almost minimal boundaries are smooth. This can be viewed as a non-local ver...
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| creator | Caputo, M. Cristina Guillen, Nestor |
| description | We introduce a notion of non-local almost minimal boundaries similar to that
introduced by Almgren in geometric measure theory. Extending methods developed
recently for non-local minimal surfaces we prove that flat non-local almost
minimal boundaries are smooth. This can be viewed as a non-local version of the
Almgren-De Giorgi-Tamanini regularity theory. The main result has several
applications, among these $C^{1,\alpha}$ regularity for sets with prescribed
non-local mean curvature in $L^p$ and regularity of solutions to non-local
obstacle problems. |
| doi_str_mv | 10.48550/arxiv.1003.2470 |
| format | Article |
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introduced by Almgren in geometric measure theory. Extending methods developed
recently for non-local minimal surfaces we prove that flat non-local almost
minimal boundaries are smooth. This can be viewed as a non-local version of the
Almgren-De Giorgi-Tamanini regularity theory. The main result has several
applications, among these $C^{1,\alpha}$ regularity for sets with prescribed
non-local mean curvature in $L^p$ and regularity of solutions to non-local
obstacle problems.</description><identifier>DOI: 10.48550/arxiv.1003.2470</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs ; Mathematics - Differential Geometry</subject><creationdate>2010-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1003.2470$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1003.2470$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Caputo, M. Cristina</creatorcontrib><creatorcontrib>Guillen, Nestor</creatorcontrib><title>Regularity for non-local almost minimal boundaries and applications</title><description>We introduce a notion of non-local almost minimal boundaries similar to that
introduced by Almgren in geometric measure theory. Extending methods developed
recently for non-local minimal surfaces we prove that flat non-local almost
minimal boundaries are smooth. This can be viewed as a non-local version of the
Almgren-De Giorgi-Tamanini regularity theory. The main result has several
applications, among these $C^{1,\alpha}$ regularity for sets with prescribed
non-local mean curvature in $L^p$ and regularity of solutions to non-local
obstacle problems.</description><subject>Mathematics - Analysis of PDEs</subject><subject>Mathematics - Differential Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tqwzAURLXpoqTZd1X0A3avooedZTBNWggUSvbm6hUEsmRkpzR_H6ftahgYDnMIeWZQi1ZKeMXyE75rBsDrjWjgkXRf7nyJWMJ8pT4XmnKqYjYYKcYhTzMdQgrDUnW-JLvs3EQxWYrjGIPBOeQ0PZEHj3Fy6_9ckdP-7dS9V8fPw0e3O1aoJFQaufPMA1PWO8PcxgG3AhiYxjZCb8GoFqTVQjvhFWuU0spbI7FtHRO45Svy8of9lejHsvwq1_4u099l-A0lvkWp</recordid><startdate>20100311</startdate><enddate>20100311</enddate><creator>Caputo, M. Cristina</creator><creator>Guillen, Nestor</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20100311</creationdate><title>Regularity for non-local almost minimal boundaries and applications</title><author>Caputo, M. Cristina ; Guillen, Nestor</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a650-ba3ef1f016dfec1e2e03d4010c7d74b90c6805db4be4f61766b6fdc5a88e14a93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Mathematics - Analysis of PDEs</topic><topic>Mathematics - Differential Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Caputo, M. Cristina</creatorcontrib><creatorcontrib>Guillen, Nestor</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Caputo, M. Cristina</au><au>Guillen, Nestor</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Regularity for non-local almost minimal boundaries and applications</atitle><date>2010-03-11</date><risdate>2010</risdate><abstract>We introduce a notion of non-local almost minimal boundaries similar to that
introduced by Almgren in geometric measure theory. Extending methods developed
recently for non-local minimal surfaces we prove that flat non-local almost
minimal boundaries are smooth. This can be viewed as a non-local version of the
Almgren-De Giorgi-Tamanini regularity theory. The main result has several
applications, among these $C^{1,\alpha}$ regularity for sets with prescribed
non-local mean curvature in $L^p$ and regularity of solutions to non-local
obstacle problems.</abstract><doi>10.48550/arxiv.1003.2470</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs Mathematics - Differential Geometry |
| title | Regularity for non-local almost minimal boundaries and applications |
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