An Extension Problem Related to the Fractional Laplacian

The operator square root of the Laplacian (− ▵) 1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this article, we obtain similar characterizations for general fractional powers of t...

Full description

Saved in:
Bibliographic Details
Published in:Communications in partial differential equations 2007-08, Vol.32 (8), p.1245-1260
Main Authors: Caffarelli, Luis, Silvestre, Luis
Format: Article
Language:English
Subjects:
Degenerate elliptic equations
Fractional Laplacian
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c389t-98a7cf376649c83876fafaf8ee3f5c0ce034a6b5dbac431808e3b71453af2a4b3
cites cdi_FETCH-LOGICAL-c389t-98a7cf376649c83876fafaf8ee3f5c0ce034a6b5dbac431808e3b71453af2a4b3
container_end_page 1260
container_issue 8
container_start_page 1245
container_title Communications in partial differential equations
container_volume 32
creator Caffarelli, Luis
Silvestre, Luis
description The operator square root of the Laplacian (− ▵) 1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this article, we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some properties of these integro-differential equations from purely local arguments in the extension problems.
doi_str_mv 10.1080/03605300600987306
format article
fullrecord <record><control><sourceid>crossref_infor</sourceid><recordid>TN_cdi_informaworld_taylorfrancis_310_1080_03605300600987306</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1080_03605300600987306</sourcerecordid><originalsourceid>FETCH-LOGICAL-c389t-98a7cf376649c83876fafaf8ee3f5c0ce034a6b5dbac431808e3b71453af2a4b3</originalsourceid><addsrcrecordid>eNqFj0FLAzEQhYMoWKs_wFv-wOpkJ5vNgpdSWhUKiuh5mU0TXEk3JQnY_nu31FsReYc5vPfN4zF2K-BOgIZ7QAUVAiiARtcI6oxNRIVlIQXiOZsc_GIMlJfsKqUvAKHLRk6Yng18sct2SH0Y-GsMnbcb_mY9ZbvmOfD8afkyksmjT56vaOvJ9DRcswtHPtmb3ztlH8vF-_ypWL08Ps9nq8KgbnLRaKqNw1op2RiNulaORmlr0VUGjAWUpLpq3ZGRKDRoi10tZIXkSpIdTpk4_jUxpBSta7ex31DctwLaw_T2ZPrI1EemH1yIG_oO0a_bTHsfoos0mD6dUm3e5ZF8-JfEv4t_AMzvcHQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>An Extension Problem Related to the Fractional Laplacian</title><source>Taylor and Francis Science and Technology Collection</source><creator>Caffarelli, Luis ; Silvestre, Luis</creator><creatorcontrib>Caffarelli, Luis ; Silvestre, Luis</creatorcontrib><description>The operator square root of the Laplacian (− ▵) 1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this article, we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some properties of these integro-differential equations from purely local arguments in the extension problems.</description><identifier>ISSN: 0360-5302</identifier><identifier>EISSN: 1532-4133</identifier><identifier>DOI: 10.1080/03605300600987306</identifier><language>eng</language><publisher>Taylor &amp; Francis Group</publisher><subject>Degenerate elliptic equations ; Fractional Laplacian</subject><ispartof>Communications in partial differential equations, 2007-08, Vol.32 (8), p.1245-1260</ispartof><rights>Copyright Taylor &amp; Francis Group, LLC 2007</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c389t-98a7cf376649c83876fafaf8ee3f5c0ce034a6b5dbac431808e3b71453af2a4b3</citedby><cites>FETCH-LOGICAL-c389t-98a7cf376649c83876fafaf8ee3f5c0ce034a6b5dbac431808e3b71453af2a4b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Caffarelli, Luis</creatorcontrib><creatorcontrib>Silvestre, Luis</creatorcontrib><title>An Extension Problem Related to the Fractional Laplacian</title><title>Communications in partial differential equations</title><description>The operator square root of the Laplacian (− ▵) 1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this article, we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some properties of these integro-differential equations from purely local arguments in the extension problems.</description><subject>Degenerate elliptic equations</subject><subject>Fractional Laplacian</subject><issn>0360-5302</issn><issn>1532-4133</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNqFj0FLAzEQhYMoWKs_wFv-wOpkJ5vNgpdSWhUKiuh5mU0TXEk3JQnY_nu31FsReYc5vPfN4zF2K-BOgIZ7QAUVAiiARtcI6oxNRIVlIQXiOZsc_GIMlJfsKqUvAKHLRk6Yng18sct2SH0Y-GsMnbcb_mY9ZbvmOfD8afkyksmjT56vaOvJ9DRcswtHPtmb3ztlH8vF-_ypWL08Ps9nq8KgbnLRaKqNw1op2RiNulaORmlr0VUGjAWUpLpq3ZGRKDRoi10tZIXkSpIdTpk4_jUxpBSta7ex31DctwLaw_T2ZPrI1EemH1yIG_oO0a_bTHsfoos0mD6dUm3e5ZF8-JfEv4t_AMzvcHQ</recordid><startdate>20070808</startdate><enddate>20070808</enddate><creator>Caffarelli, Luis</creator><creator>Silvestre, Luis</creator><general>Taylor &amp; Francis Group</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20070808</creationdate><title>An Extension Problem Related to the Fractional Laplacian</title><author>Caffarelli, Luis ; Silvestre, Luis</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c389t-98a7cf376649c83876fafaf8ee3f5c0ce034a6b5dbac431808e3b71453af2a4b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Degenerate elliptic equations</topic><topic>Fractional Laplacian</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Caffarelli, Luis</creatorcontrib><creatorcontrib>Silvestre, Luis</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Caffarelli, Luis</au><au>Silvestre, Luis</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An Extension Problem Related to the Fractional Laplacian</atitle><jtitle>Communications in partial differential equations</jtitle><date>2007-08-08</date><risdate>2007</risdate><volume>32</volume><issue>8</issue><spage>1245</spage><epage>1260</epage><pages>1245-1260</pages><issn>0360-5302</issn><eissn>1532-4133</eissn><abstract>The operator square root of the Laplacian (− ▵) 1/2 can be obtained from the harmonic extension problem to the upper half space as the operator that maps the Dirichlet boundary condition to the Neumann condition. In this article, we obtain similar characterizations for general fractional powers of the Laplacian and other integro-differential operators. From those characterizations we derive some properties of these integro-differential equations from purely local arguments in the extension problems.</abstract><pub>Taylor &amp; Francis Group</pub><doi>10.1080/03605300600987306</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0360-5302
ispartof Communications in partial differential equations, 2007-08, Vol.32 (8), p.1245-1260
issn 0360-5302
1532-4133
language eng
recordid cdi_informaworld_taylorfrancis_310_1080_03605300600987306
source Taylor and Francis Science and Technology Collection
subjects Degenerate elliptic equations
Fractional Laplacian
title An Extension Problem Related to the Fractional Laplacian
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T05%3A28%3A18IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-crossref_infor&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=An%20Extension%20Problem%20Related%20to%20the%20Fractional%20Laplacian&rft.jtitle=Communications%20in%20partial%20differential%20equations&rft.au=Caffarelli,%20Luis&rft.date=2007-08-08&rft.volume=32&rft.issue=8&rft.spage=1245&rft.epage=1260&rft.pages=1245-1260&rft.issn=0360-5302&rft.eissn=1532-4133&rft_id=info:doi/10.1080/03605300600987306&rft_dat=%3Ccrossref_infor%3E10_1080_03605300600987306%3C/crossref_infor%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c389t-98a7cf376649c83876fafaf8ee3f5c0ce034a6b5dbac431808e3b71453af2a4b3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true