Loading…

The existence of k-convex hypersurface with prescribed mean curvature

Using the strong maximum principle, we obtain a constant rank theorem for the k -convex solutions of semilinear elliptic partial differential equations. As an application we obtain an existence theorem of k -convex starshaped hypersurface with prescribed mean curvature in R n +1 .

Saved in:
Bibliographic Details
Published in:Calculus of variations and partial differential equations 2011-09, Vol.42 (1-2), p.43-72
Main Authors: Han, Fei, Ma, Xi-Nan, Wu, Damin
Format: Article
Language:English
Subjects:
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c347t-e9497ed1de85fcd4b8e27e773703b0bf8065789ac5e12e1c50c4e8acfb363d0d3
cites cdi_FETCH-LOGICAL-c347t-e9497ed1de85fcd4b8e27e773703b0bf8065789ac5e12e1c50c4e8acfb363d0d3
container_end_page 72
container_issue 1-2
container_start_page 43
container_title Calculus of variations and partial differential equations
container_volume 42
creator Han, Fei
Ma, Xi-Nan
Wu, Damin
description Using the strong maximum principle, we obtain a constant rank theorem for the k -convex solutions of semilinear elliptic partial differential equations. As an application we obtain an existence theorem of k -convex starshaped hypersurface with prescribed mean curvature in R n +1 .
doi_str_mv 10.1007/s00526-010-0379-2
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_896192418</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>896192418</sourcerecordid><originalsourceid>FETCH-LOGICAL-c347t-e9497ed1de85fcd4b8e27e773703b0bf8065789ac5e12e1c50c4e8acfb363d0d3</originalsourceid><addsrcrecordid>eNp1kEtLw0AUhQdRsFZ_gLvgxtXonVdmZimlPqDgpq6HZHJjU9skziS1_femRBAEV3dxvnO4fIRcM7hjAPo-AiieUmBAQWhL-QmZMCk4BSPUKZmAlZLyNLXn5CLGNQBThssJmS9XmOC-ih3WHpOmTD6ob-od7pPVocUQ-1BmQ_BVdaukDRh9qHIski1mdeL7sMu6PuAlOSuzTcSrnzslb4_z5eyZLl6fXmYPC-qF1B1FK63GghVoVOkLmRvkGrUWGkQOeWkgVdrYzCtkHJlX4CWazJe5SEUBhZiS23G3Dc1nj7Fz2yp63GyyGps-OmNTZrlkZiBv_pDrpg_18JwzWhulQMsBYiPkQxNjwNK1odpm4eAYuKNWN2p1g1Z31Or40OFjJw5s_Y7hd_j_0jdBFHqa</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>877855074</pqid></control><display><type>article</type><title>The existence of k-convex hypersurface with prescribed mean curvature</title><source>Springer Nature</source><creator>Han, Fei ; Ma, Xi-Nan ; Wu, Damin</creator><creatorcontrib>Han, Fei ; Ma, Xi-Nan ; Wu, Damin</creatorcontrib><description>Using the strong maximum principle, we obtain a constant rank theorem for the k -convex solutions of semilinear elliptic partial differential equations. As an application we obtain an existence theorem of k -convex starshaped hypersurface with prescribed mean curvature in R n +1 .</description><identifier>ISSN: 0944-2669</identifier><identifier>EISSN: 1432-0835</identifier><identifier>DOI: 10.1007/s00526-010-0379-2</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Analysis ; Calculus ; Calculus of variations ; Calculus of Variations and Optimal Control; Optimization ; Control ; Curvature ; Existence theorems ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Maximum principle ; Partial differential equations ; Systems Theory ; Theorems ; Theoretical</subject><ispartof>Calculus of variations and partial differential equations, 2011-09, Vol.42 (1-2), p.43-72</ispartof><rights>Springer-Verlag 2010</rights><rights>Springer-Verlag 2011</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c347t-e9497ed1de85fcd4b8e27e773703b0bf8065789ac5e12e1c50c4e8acfb363d0d3</citedby><cites>FETCH-LOGICAL-c347t-e9497ed1de85fcd4b8e27e773703b0bf8065789ac5e12e1c50c4e8acfb363d0d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>Han, Fei</creatorcontrib><creatorcontrib>Ma, Xi-Nan</creatorcontrib><creatorcontrib>Wu, Damin</creatorcontrib><title>The existence of k-convex hypersurface with prescribed mean curvature</title><title>Calculus of variations and partial differential equations</title><addtitle>Calc. Var</addtitle><description>Using the strong maximum principle, we obtain a constant rank theorem for the k -convex solutions of semilinear elliptic partial differential equations. As an application we obtain an existence theorem of k -convex starshaped hypersurface with prescribed mean curvature in R n +1 .</description><subject>Analysis</subject><subject>Calculus</subject><subject>Calculus of variations</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Control</subject><subject>Curvature</subject><subject>Existence theorems</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Maximum principle</subject><subject>Partial differential equations</subject><subject>Systems Theory</subject><subject>Theorems</subject><subject>Theoretical</subject><issn>0944-2669</issn><issn>1432-0835</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLw0AUhQdRsFZ_gLvgxtXonVdmZimlPqDgpq6HZHJjU9skziS1_femRBAEV3dxvnO4fIRcM7hjAPo-AiieUmBAQWhL-QmZMCk4BSPUKZmAlZLyNLXn5CLGNQBThssJmS9XmOC-ih3WHpOmTD6ob-od7pPVocUQ-1BmQ_BVdaukDRh9qHIski1mdeL7sMu6PuAlOSuzTcSrnzslb4_z5eyZLl6fXmYPC-qF1B1FK63GghVoVOkLmRvkGrUWGkQOeWkgVdrYzCtkHJlX4CWazJe5SEUBhZiS23G3Dc1nj7Fz2yp63GyyGps-OmNTZrlkZiBv_pDrpg_18JwzWhulQMsBYiPkQxNjwNK1odpm4eAYuKNWN2p1g1Z31Or40OFjJw5s_Y7hd_j_0jdBFHqa</recordid><startdate>20110901</startdate><enddate>20110901</enddate><creator>Han, Fei</creator><creator>Ma, Xi-Nan</creator><creator>Wu, Damin</creator><general>Springer-Verlag</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20110901</creationdate><title>The existence of k-convex hypersurface with prescribed mean curvature</title><author>Han, Fei ; Ma, Xi-Nan ; Wu, Damin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c347t-e9497ed1de85fcd4b8e27e773703b0bf8065789ac5e12e1c50c4e8acfb363d0d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Analysis</topic><topic>Calculus</topic><topic>Calculus of variations</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Control</topic><topic>Curvature</topic><topic>Existence theorems</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Maximum principle</topic><topic>Partial differential equations</topic><topic>Systems Theory</topic><topic>Theorems</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Han, Fei</creatorcontrib><creatorcontrib>Ma, Xi-Nan</creatorcontrib><creatorcontrib>Wu, Damin</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Calculus of variations and partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Han, Fei</au><au>Ma, Xi-Nan</au><au>Wu, Damin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The existence of k-convex hypersurface with prescribed mean curvature</atitle><jtitle>Calculus of variations and partial differential equations</jtitle><stitle>Calc. Var</stitle><date>2011-09-01</date><risdate>2011</risdate><volume>42</volume><issue>1-2</issue><spage>43</spage><epage>72</epage><pages>43-72</pages><issn>0944-2669</issn><eissn>1432-0835</eissn><abstract>Using the strong maximum principle, we obtain a constant rank theorem for the k -convex solutions of semilinear elliptic partial differential equations. As an application we obtain an existence theorem of k -convex starshaped hypersurface with prescribed mean curvature in R n +1 .</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s00526-010-0379-2</doi><tpages>30</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0944-2669
ispartof Calculus of variations and partial differential equations, 2011-09, Vol.42 (1-2), p.43-72
issn 0944-2669
1432-0835
language eng
recordid cdi_proquest_miscellaneous_896192418
source Springer Nature
subjects Analysis
Calculus
Calculus of variations
Calculus of Variations and Optimal Control
Optimization
Control
Curvature
Existence theorems
Mathematical analysis
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Maximum principle
Partial differential equations
Systems Theory
Theorems
Theoretical
title The existence of k-convex hypersurface with prescribed mean curvature
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-23T22%3A23%3A58IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20existence%20of%20k-convex%20hypersurface%20with%20prescribed%20mean%20curvature&rft.jtitle=Calculus%20of%20variations%20and%20partial%20differential%20equations&rft.au=Han,%20Fei&rft.date=2011-09-01&rft.volume=42&rft.issue=1-2&rft.spage=43&rft.epage=72&rft.pages=43-72&rft.issn=0944-2669&rft.eissn=1432-0835&rft_id=info:doi/10.1007/s00526-010-0379-2&rft_dat=%3Cproquest_cross%3E896192418%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c347t-e9497ed1de85fcd4b8e27e773703b0bf8065789ac5e12e1c50c4e8acfb363d0d3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=877855074&rft_id=info:pmid/&rfr_iscdi=true