Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations
We consider overdetermined problems for Hessian quotient equations and Hessian quotient curvature equations, which are fully nonlinear elliptic equations. We establish Rellich–Pohozaev-type identities for Hessian quotient equations and Hessian quotient curvature equations. Based on these identities...
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| Veröffentlicht in: | The Journal of Geometric Analysis 2023-05, Vol.33 (5), Article 150 |
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| container_title | The Journal of Geometric Analysis |
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| creator | Gao, Zhenghuan Jia, Xiaohan Zhang, Dekai |
| description | We consider overdetermined problems for Hessian quotient equations and Hessian quotient curvature equations, which are fully nonlinear elliptic equations. We establish Rellich–Pohozaev-type identities for Hessian quotient equations and Hessian quotient curvature equations. Based on these identities and the maximum principle for
P
functions, the symmetry of solutions can be proved in the Euclidean space. We also prove the related result for Hessian quotient equations in the hyperbolic space. Our results generalize the overdetermined problems for
k
-Hessian equations and
k
-curvature equations. |
| doi_str_mv | 10.1007/s12220-023-01198-w |
| format | Article |
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P
functions, the symmetry of solutions can be proved in the Euclidean space. We also prove the related result for Hessian quotient equations in the hyperbolic space. Our results generalize the overdetermined problems for
k
-Hessian equations and
k
-curvature equations.</description><identifier>ISSN: 1050-6926</identifier><identifier>EISSN: 1559-002X</identifier><identifier>DOI: 10.1007/s12220-023-01198-w</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Abstract Harmonic Analysis ; Convex and Discrete Geometry ; Curvature ; Differential Geometry ; Dynamical Systems and Ergodic Theory ; Elliptic functions ; Euclidean geometry ; Fourier Analysis ; Geometry ; Global Analysis and Analysis on Manifolds ; Hyperbolic coordinates ; Identities ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Maximum principle ; Quotients</subject><ispartof>The Journal of Geometric Analysis, 2023-05, Vol.33 (5), Article 150</ispartof><rights>Mathematica Josephina, Inc. 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><rights>COPYRIGHT 2023 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c239t-9db9460b40f180f2517cbec4f5ba9f9eac779b86811f6c7c6b768e3b30adb50f3</cites><orcidid>0000-0002-9631-5386</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/s12220-023-01198-w$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12220-023-01198-w$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Gao, Zhenghuan</creatorcontrib><creatorcontrib>Jia, Xiaohan</creatorcontrib><creatorcontrib>Zhang, Dekai</creatorcontrib><title>Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations</title><title>The Journal of Geometric Analysis</title><addtitle>J Geom Anal</addtitle><description>We consider overdetermined problems for Hessian quotient equations and Hessian quotient curvature equations, which are fully nonlinear elliptic equations. We establish Rellich–Pohozaev-type identities for Hessian quotient equations and Hessian quotient curvature equations. Based on these identities and the maximum principle for
P
functions, the symmetry of solutions can be proved in the Euclidean space. We also prove the related result for Hessian quotient equations in the hyperbolic space. Our results generalize the overdetermined problems for
k
-Hessian equations and
k
-curvature equations.</description><subject>Abstract Harmonic Analysis</subject><subject>Convex and Discrete Geometry</subject><subject>Curvature</subject><subject>Differential Geometry</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Elliptic functions</subject><subject>Euclidean geometry</subject><subject>Fourier Analysis</subject><subject>Geometry</subject><subject>Global Analysis and Analysis on Manifolds</subject><subject>Hyperbolic coordinates</subject><subject>Identities</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Maximum principle</subject><subject>Quotients</subject><issn>1050-6926</issn><issn>1559-002X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kcFqGzEQhkVpoamTF-hpoWelI2l3tToak9aFQBKSQm5C0o6CUltypN0Yv33W3YIPhWgOGmb-b2bgJ-Qrg0sGIL8XxjkHClxQYEx1dP-BnLGmURSAP36ccmiAtoq3n8mXUp4B6lbU8oz8ucecQ6QPhx1WN6-Yexwwb0PEvrrNyW5wWyqfcrXGUoKJ1d2YhoBxqK5eRjOEFEtlYv9_ezXmVzOMGU_Cc_LJm03Bi3__gvz-cfWwWtPrm5-_Vstr6rhQA1W9VXULtgbPOvC8YdJZdLVvrFFeoXFSKtu1HWO-ddK1VrYdCivA9LYBLxbk2zx3l9PLiGXQz2nMcVqpueygq8XxLcjlrHoyG9Qh-jRk46bocRtciujDVF9KoaATUMME8BlwOZWS0etdDluTD5qBPrqgZxf05IL-64LeT5CYoTKJ4xPm0y3vUG-YsozX</recordid><startdate>20230501</startdate><enddate>20230501</enddate><creator>Gao, Zhenghuan</creator><creator>Jia, Xiaohan</creator><creator>Zhang, Dekai</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>IAO</scope><orcidid>https://orcid.org/0000-0002-9631-5386</orcidid></search><sort><creationdate>20230501</creationdate><title>Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations</title><author>Gao, Zhenghuan ; Jia, Xiaohan ; Zhang, Dekai</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c239t-9db9460b40f180f2517cbec4f5ba9f9eac779b86811f6c7c6b768e3b30adb50f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Convex and Discrete Geometry</topic><topic>Curvature</topic><topic>Differential Geometry</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Elliptic functions</topic><topic>Euclidean geometry</topic><topic>Fourier Analysis</topic><topic>Geometry</topic><topic>Global Analysis and Analysis on Manifolds</topic><topic>Hyperbolic coordinates</topic><topic>Identities</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Maximum principle</topic><topic>Quotients</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gao, Zhenghuan</creatorcontrib><creatorcontrib>Jia, Xiaohan</creatorcontrib><creatorcontrib>Zhang, Dekai</creatorcontrib><collection>CrossRef</collection><collection>Gale Academic OneFile</collection><jtitle>The Journal of Geometric Analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gao, Zhenghuan</au><au>Jia, Xiaohan</au><au>Zhang, Dekai</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations</atitle><jtitle>The Journal of Geometric Analysis</jtitle><stitle>J Geom Anal</stitle><date>2023-05-01</date><risdate>2023</risdate><volume>33</volume><issue>5</issue><artnum>150</artnum><issn>1050-6926</issn><eissn>1559-002X</eissn><abstract>We consider overdetermined problems for Hessian quotient equations and Hessian quotient curvature equations, which are fully nonlinear elliptic equations. We establish Rellich–Pohozaev-type identities for Hessian quotient equations and Hessian quotient curvature equations. Based on these identities and the maximum principle for
P
functions, the symmetry of solutions can be proved in the Euclidean space. We also prove the related result for Hessian quotient equations in the hyperbolic space. Our results generalize the overdetermined problems for
k
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k
-curvature equations.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s12220-023-01198-w</doi><orcidid>https://orcid.org/0000-0002-9631-5386</orcidid></addata></record> |
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| subjects | Abstract Harmonic Analysis Convex and Discrete Geometry Curvature Differential Geometry Dynamical Systems and Ergodic Theory Elliptic functions Euclidean geometry Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Hyperbolic coordinates Identities Mathematical analysis Mathematics Mathematics and Statistics Maximum principle Quotients |
| title | Serrin-Type Overdetermined Problems for Hessian Quotient Equations and Hessian Quotient Curvature Equations |
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