Allard-type boundary regularity for $C^{1,\alpha}$ boundaries
In this paper we show boundary monotonicity formulae for rectifiable varifolds having a $C^{1,\alpha}$ "boundary". In particular, we show that the area ratios of balls centered at this "boundary'' satisfy a nice monotonicity formula, similar to that for interior balls (prove...
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| creator | Bourni, Theodora |
| description | In this paper we show boundary monotonicity formulae for rectifiable
varifolds having a $C^{1,\alpha}$ "boundary". In particular, we show that the
area ratios of balls centered at this "boundary'' satisfy a nice monotonicity
formula, similar to that for interior balls (proved in Allard's paper "On the
first variation of a varifold''). This extends the boundary monotonicity
formulae of Allard (see "On the first variation of a varifold- boundary
behavior''), which require that the boundary is $C^{1,1}$. As a corollary,
Allard's boundary regularity results extend to this case and provide a
regularity result for rectifiable varifolds with a $C^{1,\alpha}$ ``boundary''. |
| doi_str_mv | 10.48550/arxiv.1008.4728 |
| format | Article |
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varifolds having a $C^{1,\alpha}$ "boundary". In particular, we show that the
area ratios of balls centered at this "boundary'' satisfy a nice monotonicity
formula, similar to that for interior balls (proved in Allard's paper "On the
first variation of a varifold''). This extends the boundary monotonicity
formulae of Allard (see "On the first variation of a varifold- boundary
behavior''), which require that the boundary is $C^{1,1}$. As a corollary,
Allard's boundary regularity results extend to this case and provide a
regularity result for rectifiable varifolds with a $C^{1,\alpha}$ ``boundary''.</description><identifier>DOI: 10.48550/arxiv.1008.4728</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2010-08</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1008.4728$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1008.4728$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Bourni, Theodora</creatorcontrib><title>Allard-type boundary regularity for $C^{1,\alpha}$ boundaries</title><description>In this paper we show boundary monotonicity formulae for rectifiable
varifolds having a $C^{1,\alpha}$ "boundary". In particular, we show that the
area ratios of balls centered at this "boundary'' satisfy a nice monotonicity
formula, similar to that for interior balls (proved in Allard's paper "On the
first variation of a varifold''). This extends the boundary monotonicity
formulae of Allard (see "On the first variation of a varifold- boundary
behavior''), which require that the boundary is $C^{1,1}$. As a corollary,
Allard's boundary regularity results extend to this case and provide a
regularity result for rectifiable varifolds with a $C^{1,\alpha}$ ``boundary''.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNo1j79Lw1AUhd_SQVp3J8nQsYn3Je_HzdChBK2FgktGMdy83KeBtA2vrRik_7ut1enA4XD4PiHuJCQKtYYHCl_tZyIBMFE2xRsxX3QdhSY-DD1H9e64bSgMUeD347luD0PkdyGaFm_fcvZKXf9Bp-n_rOX9RIw8dXu-_cuxKJ8ey-I5Xr8sV8ViHZPRGHvLprYyVY41aOcMMKBRgA4sUtN4m0unWEKae6sAMoNIOdQarGaTYTYW99fbX_yqD-3mTFldNKqLRvYDYtpBGA</recordid><startdate>20100827</startdate><enddate>20100827</enddate><creator>Bourni, Theodora</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20100827</creationdate><title>Allard-type boundary regularity for $C^{1,\alpha}$ boundaries</title><author>Bourni, Theodora</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a658-f7e6b7124ce505cc60e086408c078addf791c4e1029f74003688a90b5075e6383</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Bourni, Theodora</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Bourni, Theodora</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Allard-type boundary regularity for $C^{1,\alpha}$ boundaries</atitle><date>2010-08-27</date><risdate>2010</risdate><abstract>In this paper we show boundary monotonicity formulae for rectifiable
varifolds having a $C^{1,\alpha}$ "boundary". In particular, we show that the
area ratios of balls centered at this "boundary'' satisfy a nice monotonicity
formula, similar to that for interior balls (proved in Allard's paper "On the
first variation of a varifold''). This extends the boundary monotonicity
formulae of Allard (see "On the first variation of a varifold- boundary
behavior''), which require that the boundary is $C^{1,1}$. As a corollary,
Allard's boundary regularity results extend to this case and provide a
regularity result for rectifiable varifolds with a $C^{1,\alpha}$ ``boundary''.</abstract><doi>10.48550/arxiv.1008.4728</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Allard-type boundary regularity for $C^{1,\alpha}$ boundaries |
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