Equivalence of solutions to fractional $p$-Laplace type equations
In this paper, we study different notions of solutions of nonlocal and nonlinear equations of fractional $p$-Laplace type $${\rm P.V.} \int_{\mathbb R^n}\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}\,dy = 0.$$ Solutions are defined via integration by parts with test functions, as viscosity solut...
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| creator | Korvenpää, Janne Kuusi, Tuomo Lindgren, Erik |
| description | In this paper, we study different notions of solutions of nonlocal and
nonlinear equations of fractional $p$-Laplace type $${\rm P.V.} \int_{\mathbb
R^n}\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}\,dy = 0.$$ Solutions are
defined via integration by parts with test functions, as viscosity solutions or
via comparison. Our main result states that for bounded solutions, the three
different notions coincide. |
| doi_str_mv | 10.48550/arxiv.1605.03455 |
| format | Article |
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nonlinear equations of fractional $p$-Laplace type $${\rm P.V.} \int_{\mathbb
R^n}\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}\,dy = 0.$$ Solutions are
defined via integration by parts with test functions, as viscosity solutions or
via comparison. Our main result states that for bounded solutions, the three
different notions coincide.</description><identifier>DOI: 10.48550/arxiv.1605.03455</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2016-05</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/1605.03455$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1605.03455$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Korvenpää, Janne</creatorcontrib><creatorcontrib>Kuusi, Tuomo</creatorcontrib><creatorcontrib>Lindgren, Erik</creatorcontrib><title>Equivalence of solutions to fractional $p$-Laplace type equations</title><description>In this paper, we study different notions of solutions of nonlocal and
nonlinear equations of fractional $p$-Laplace type $${\rm P.V.} \int_{\mathbb
R^n}\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}\,dy = 0.$$ Solutions are
defined via integration by parts with test functions, as viscosity solutions or
via comparison. Our main result states that for bounded solutions, the three
different notions coincide.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj7kKwkAURaexEPUDrJzCNnG258uUIm4QsLEPz3ECgdHELKJ_r0ary4XDgcPYVIrYJABiQfWzeMRyKSAW2gAM2Wpz74oHBX9znpc5b8rQtUV5a3hb8rwm9z0U-LyaRylVgT5Y-6o89_eOenDMBjmFxk_-O2Kn7ea03kfpcXdYr9KIlgiRdM5YnXhCQIfmIhJUBu1ZgiKSCJAIq6QhtFZLNKBRGwHCqbNXElHpEZv9tH1DVtXFlepX9m3J-hb9BuoqQgg</recordid><startdate>20160511</startdate><enddate>20160511</enddate><creator>Korvenpää, Janne</creator><creator>Kuusi, Tuomo</creator><creator>Lindgren, Erik</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20160511</creationdate><title>Equivalence of solutions to fractional $p$-Laplace type equations</title><author>Korvenpää, Janne ; Kuusi, Tuomo ; Lindgren, Erik</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a675-1cc4938ea757c74d0872479b152aa1755809214a799317453734050c2be217723</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Korvenpää, Janne</creatorcontrib><creatorcontrib>Kuusi, Tuomo</creatorcontrib><creatorcontrib>Lindgren, Erik</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Korvenpää, Janne</au><au>Kuusi, Tuomo</au><au>Lindgren, Erik</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Equivalence of solutions to fractional $p$-Laplace type equations</atitle><date>2016-05-11</date><risdate>2016</risdate><abstract>In this paper, we study different notions of solutions of nonlocal and
nonlinear equations of fractional $p$-Laplace type $${\rm P.V.} \int_{\mathbb
R^n}\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{n+sp}}\,dy = 0.$$ Solutions are
defined via integration by parts with test functions, as viscosity solutions or
via comparison. Our main result states that for bounded solutions, the three
different notions coincide.</abstract><doi>10.48550/arxiv.1605.03455</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Equivalence of solutions to fractional $p$-Laplace type equations |
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