The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions
We discuss existence, uniqueness, regularity and boundary behaviour of solutions of the Dirichlet problem for the prescribed anisotropic mean curvature equation−div(∇u/1+|∇u|2)=−au+b/1+|∇u|2, where a,b>0 are given parameters and Ω is a bounded Lipschitz domain in RN. This equation appears in the...
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| Veröffentlicht in: | Journal of Differential Equations 2016-03, Vol.260 (5), p.4572-4618 |
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| container_title | Journal of Differential Equations |
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| creator | Corsato, Chiara De Coster, Colette Omari, Pierpaolo |
| description | We discuss existence, uniqueness, regularity and boundary behaviour of solutions of the Dirichlet problem for the prescribed anisotropic mean curvature equation−div(∇u/1+|∇u|2)=−au+b/1+|∇u|2, where a,b>0 are given parameters and Ω is a bounded Lipschitz domain in RN. This equation appears in the modeling theory of capillarity phenomena for compressible fluids and in the description of the geometry of the human cornea. |
| doi_str_mv | 10.1016/j.jde.2015.11.024 |
| format | Article |
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This equation appears in the modeling theory of capillarity phenomena for compressible fluids and in the description of the geometry of the human cornea.</description><subject>Boundary behaviour</subject><subject>Bounded variation function</subject><subject>Dirichlet boundary condition</subject><subject>Existence</subject><subject>Mathematics</subject><subject>Positive solution</subject><subject>Prescribed anisotropic mean curvature equation</subject><subject>Regularity</subject><subject>Uniqueness</subject><subject>Variational methods</subject><issn>0022-0396</issn><issn>1090-2732</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAQhi0EEqXwA9i8IpFgO3ESw1TxVaRKLGW2HPtCXaVxazsVHfjvJCpiZDq9p_c56R6ErilJKaHF3TpdG0gZoTylNCUsP0ETSgRJWJmxUzQhhLGEZKI4RxchrAmhlBd8gr6XK8BP1lu9aiHirXd1CxvcOI_VkCBob2swWHU2uOjd1mq8AdVh3fu9ir0HDLteReu6ewxfNkToNNzivrO7HjoIYUAN9vDZt8rbeMCuwcG1_UiES3TWqDbA1e-coo-X5-XjPFm8v749zhaJzso8JqoRjPOs4gRMU9YVUxwIz4QSua5qpQwXpdBQ5aUYmnlecEXKhjGjBSuNNtkU3RzvrlQrt95ulD9Ip6yczxZy3JGMZryifE-HLj12tXcheGj-AErk6Fqu5eBajq4lpXJwPTAPRwaGJ_YWvAzajiKM9aCjNM7-Q_8AM4KJew</recordid><startdate>20160305</startdate><enddate>20160305</enddate><creator>Corsato, Chiara</creator><creator>De Coster, Colette</creator><creator>Omari, Pierpaolo</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-5230-7704</orcidid></search><sort><creationdate>20160305</creationdate><title>The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions</title><author>Corsato, Chiara ; De Coster, Colette ; Omari, Pierpaolo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c374t-af92553850edf7b82a5e0539a94c8baad5979ce8479f924465a07f22dc927dcd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Boundary behaviour</topic><topic>Bounded variation function</topic><topic>Dirichlet boundary condition</topic><topic>Existence</topic><topic>Mathematics</topic><topic>Positive solution</topic><topic>Prescribed anisotropic mean curvature equation</topic><topic>Regularity</topic><topic>Uniqueness</topic><topic>Variational methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Corsato, Chiara</creatorcontrib><creatorcontrib>De Coster, Colette</creatorcontrib><creatorcontrib>Omari, Pierpaolo</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Journal of Differential Equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Corsato, Chiara</au><au>De Coster, Colette</au><au>Omari, Pierpaolo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions</atitle><jtitle>Journal of Differential Equations</jtitle><date>2016-03-05</date><risdate>2016</risdate><volume>260</volume><issue>5</issue><spage>4572</spage><epage>4618</epage><pages>4572-4618</pages><issn>0022-0396</issn><eissn>1090-2732</eissn><abstract>We discuss existence, uniqueness, regularity and boundary behaviour of solutions of the Dirichlet problem for the prescribed anisotropic mean curvature equation−div(∇u/1+|∇u|2)=−au+b/1+|∇u|2, where a,b>0 are given parameters and Ω is a bounded Lipschitz domain in RN. 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| ispartof | Journal of Differential Equations, 2016-03, Vol.260 (5), p.4572-4618 |
| issn | 0022-0396 1090-2732 |
| language | eng |
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| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Boundary behaviour Bounded variation function Dirichlet boundary condition Existence Mathematics Positive solution Prescribed anisotropic mean curvature equation Regularity Uniqueness Variational methods |
| title | The Dirichlet problem for a prescribed anisotropic mean curvature equation: existence, uniqueness and regularity of solutions |
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