Nonlocal equations with gradient constraints
We prove the existence and C 1 , α regularity of solutions to nonlocal fully nonlinear elliptic equations with gradient constraints. We do not assume any regularity about the constraints; so the constraints need not be C 1 or strictly convex. We also obtain C 0 , 1 boundary regularity for these prob...
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| Veröffentlicht in: | Calculus of variations and partial differential equations 2023-09, Vol.62 (7), Article 193 |
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| container_title | Calculus of variations and partial differential equations |
| container_volume | 62 |
| creator | Safdari, Mohammad |
| description | We prove the existence and
C
1
,
α
regularity of solutions to nonlocal fully nonlinear elliptic equations with gradient constraints. We do not assume any regularity about the constraints; so the constraints need not be
C
1
or strictly convex. We also obtain
C
0
,
1
boundary regularity for these problems. Our approach is to show that these nonlocal equations with gradient constraints are related to some nonlocal double obstacle problems. Then we prove the regularity of the double obstacle problems. In this process, we also employ the monotonicity property for the second derivative of obstacles, which we have obtained in a previous work. |
| doi_str_mv | 10.1007/s00526-023-02536-0 |
| format | Article |
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C
1
,
α
regularity of solutions to nonlocal fully nonlinear elliptic equations with gradient constraints. We do not assume any regularity about the constraints; so the constraints need not be
C
1
or strictly convex. We also obtain
C
0
,
1
boundary regularity for these problems. Our approach is to show that these nonlocal equations with gradient constraints are related to some nonlocal double obstacle problems. Then we prove the regularity of the double obstacle problems. In this process, we also employ the monotonicity property for the second derivative of obstacles, which we have obtained in a previous work.</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-023-02536-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Analysis ; Barriers ; Calculus of Variations and Optimal Control; Optimization ; Control ; Elliptic functions ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Regularity ; Systems Theory ; Theoretical</subject><ispartof>Calculus of variations and partial differential equations, 2023-09, Vol.62 (7), Article 193</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c270t-cdf8a8ee1c12c8c386f15813e2990f20aa5af7fc0766eadc183829f810bc2e8b3</cites><orcidid>0000-0002-4450-1451</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00526-023-02536-0$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00526-023-02536-0$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Safdari, Mohammad</creatorcontrib><title>Nonlocal equations with gradient constraints</title><title>Calculus of variations and partial differential equations</title><addtitle>Calc. Var</addtitle><description>We prove the existence and
C
1
,
α
regularity of solutions to nonlocal fully nonlinear elliptic equations with gradient constraints. We do not assume any regularity about the constraints; so the constraints need not be
C
1
or strictly convex. We also obtain
C
0
,
1
boundary regularity for these problems. Our approach is to show that these nonlocal equations with gradient constraints are related to some nonlocal double obstacle problems. Then we prove the regularity of the double obstacle problems. In this process, we also employ the monotonicity property for the second derivative of obstacles, which we have obtained in a previous work.</description><subject>Analysis</subject><subject>Barriers</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Elliptic functions</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Regularity</subject><subject>Systems Theory</subject><subject>Theoretical</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9UEtLxDAQDqJgXf0DngperU4mbZoeZfEFi170HLJpsnapyW6SIv57oxW8eZgHw_dgPkLOKVxRgPY6AjTIK0CWq2F5OyAFrRlWIFhzSAro6rpCzrtjchLjFoA2AuuCXD55N3qtxtLsJ5UG72L5MaS3chNUPxiXSp1PKajBpXhKjqwaozn7nQvyenf7snyoVs_3j8ubVaWxhVTp3goljKGaohaaCW6zG2UGuw4sglKNsq3V0HJuVK-pYAI7KyisNRqxZgtyMevugt9PJia59VNw2VJifqfJDXlG4YzSwccYjJW7MLyr8CkpyO9U5JyKzKnIn1QkZBKbSTGD3caEP-l_WF_8ZmSR</recordid><startdate>20230901</startdate><enddate>20230901</enddate><creator>Safdari, Mohammad</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><orcidid>https://orcid.org/0000-0002-4450-1451</orcidid></search><sort><creationdate>20230901</creationdate><title>Nonlocal equations with gradient constraints</title><author>Safdari, Mohammad</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-cdf8a8ee1c12c8c386f15813e2990f20aa5af7fc0766eadc183829f810bc2e8b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Analysis</topic><topic>Barriers</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Elliptic functions</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Regularity</topic><topic>Systems Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Safdari, Mohammad</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Calculus of variations and partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Safdari, Mohammad</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonlocal equations with gradient constraints</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2023-09-01</date><risdate>2023</risdate><volume>62</volume><issue>7</issue><artnum>193</artnum><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>We prove the existence and
C
1
,
α
regularity of solutions to nonlocal fully nonlinear elliptic equations with gradient constraints. We do not assume any regularity about the constraints; so the constraints need not be
C
1
or strictly convex. We also obtain
C
0
,
1
boundary regularity for these problems. Our approach is to show that these nonlocal equations with gradient constraints are related to some nonlocal double obstacle problems. Then we prove the regularity of the double obstacle problems. In this process, we also employ the monotonicity property for the second derivative of obstacles, which we have obtained in a previous work.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00526-023-02536-0</doi><orcidid>https://orcid.org/0000-0002-4450-1451</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0944-2669 |
| ispartof | Calculus of variations and partial differential equations, 2023-09, Vol.62 (7), Article 193 |
| issn | 0944-2669 1432-0835 |
| language | eng |
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| source | SpringerLink Journals |
| subjects | Analysis Barriers Calculus of Variations and Optimal Control Optimization Control Elliptic functions Mathematical analysis Mathematical and Computational Physics Mathematics Mathematics and Statistics Regularity Systems Theory Theoretical |
| title | Nonlocal equations with gradient constraints |
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