Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations
We deal with a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order $s\in (0,1)$ and summability growth $p>1$, whose model is the fractional $p$-Laplacian with measurable coefficients. We state and prove several results for the corr...
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| creator | Korvenpaa, Janne Kuusi, Tuomo Palatucci, Giampiero |
| description | We deal with a class of equations driven by nonlocal, possibly degenerate,
integro-differential operators of differentiability order $s\in (0,1)$ and
summability growth $p>1$, whose model is the fractional $p$-Laplacian with
measurable coefficients. We state and prove several results for the
corresponding weak supersolutions, as comparison principles, a priori bounds,
lower semicontinuity, and many others. We then discuss the good definition of
$(s,p)$-superharmonic functions, by also proving some related properties. We
finally introduce the nonlocal counterpart of the celebrated Perron method in
nonlinear Potential Theory. |
| doi_str_mv | 10.48550/arxiv.1605.00906 |
| format | Article |
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integro-differential operators of differentiability order $s\in (0,1)$ and
summability growth $p>1$, whose model is the fractional $p$-Laplacian with
measurable coefficients. We state and prove several results for the
corresponding weak supersolutions, as comparison principles, a priori bounds,
lower semicontinuity, and many others. We then discuss the good definition of
$(s,p)$-superharmonic functions, by also proving some related properties. We
finally introduce the nonlocal counterpart of the celebrated Perron method in
nonlinear Potential Theory.</description><identifier>DOI: 10.48550/arxiv.1605.00906</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,778,883</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1605.00906$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1605.00906$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Korvenpaa, Janne</creatorcontrib><creatorcontrib>Kuusi, Tuomo</creatorcontrib><creatorcontrib>Palatucci, Giampiero</creatorcontrib><title>Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations</title><description>We deal with a class of equations driven by nonlocal, possibly degenerate,
integro-differential operators of differentiability order $s\in (0,1)$ and
summability growth $p>1$, whose model is the fractional $p$-Laplacian with
measurable coefficients. We state and prove several results for the
corresponding weak supersolutions, as comparison principles, a priori bounds,
lower semicontinuity, and many others. We then discuss the good definition of
$(s,p)$-superharmonic functions, by also proving some related properties. We
finally introduce the nonlocal counterpart of the celebrated Perron method in
nonlinear Potential Theory.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz7FOwzAUhWEvDKjwAEz4BRKuE9upx6qigFQJhu7RJb4mlhK73CQI3h4ITGc40i99QtwoKPXWGLhD_owfpbJgSgAH9lLQgbGbY044yGk5E_fIY06xk2FJ6zFJTF7OPckXYs5JjjT32cuQWaachpgIWcY00xvnwscQiCnN8SdI7wuuiStxEXCY6Pp_N-J0uD_tH4vj88PTfncs0Da2CBVScA0oA-gJtNZNrerKoalfwRkNxmOH3quqcUhEHYJugrbgHekObb0Rt3_Z1dmeOY7IX-2vt1299TfozFMv</recordid><startdate>20160503</startdate><enddate>20160503</enddate><creator>Korvenpaa, Janne</creator><creator>Kuusi, Tuomo</creator><creator>Palatucci, Giampiero</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20160503</creationdate><title>Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations</title><author>Korvenpaa, Janne ; Kuusi, Tuomo ; Palatucci, Giampiero</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-f2aef970150ade0444731329a53b095405dacadd1279aeeeca047f460d9e4ca63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Korvenpaa, Janne</creatorcontrib><creatorcontrib>Kuusi, Tuomo</creatorcontrib><creatorcontrib>Palatucci, Giampiero</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Korvenpaa, Janne</au><au>Kuusi, Tuomo</au><au>Palatucci, Giampiero</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations</atitle><date>2016-05-03</date><risdate>2016</risdate><abstract>We deal with a class of equations driven by nonlocal, possibly degenerate,
integro-differential operators of differentiability order $s\in (0,1)$ and
summability growth $p>1$, whose model is the fractional $p$-Laplacian with
measurable coefficients. We state and prove several results for the
corresponding weak supersolutions, as comparison principles, a priori bounds,
lower semicontinuity, and many others. We then discuss the good definition of
$(s,p)$-superharmonic functions, by also proving some related properties. We
finally introduce the nonlocal counterpart of the celebrated Perron method in
nonlinear Potential Theory.</abstract><doi>10.48550/arxiv.1605.00906</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations |
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