Dirichlet Problems for the Quasilinear Second Order Subelliptic Equations
<正> In this paper, we study the Dirichlet problems for the following quasilinear secondorder sub-elliptic equation, sum from i,j=1 to m(Xi*(Ai,j（x,u）Xj u)+sum from j=1 to m(Bj（x,u）Xj u+C（x,u）=0 in Ω, u=φ on Ω,where X={X1, …, Xm} is a system of real smooth vector fields which satisfies...
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| Veröffentlicht in: | Acta mathematica Sinica. English series 1996, Vol.12 (1), p.18-32 |
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| container_title | Acta mathematica Sinica. English series |
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| creator | Chaojiang, Xu |
| description | <正> In this paper, we study the Dirichlet problems for the following quasilinear secondorder sub-elliptic equation, sum from i,j=1 to m(Xi*(Ai,j（x,u）Xj u)+sum from j=1 to m(Bj（x,u）Xj u+C（x,u）=0 in Ω, u=φ on Ω,where X={X1, …, Xm} is a system of real smooth vector fields which satisfies the Hrmander’scondition, A（i,j）, Bj, C∈C∞（■×R） and (Ai,j（x, z）) is a positive definite matris. We have provedthe existence and the maximal regularity of solutions in the "non-isotropic" Hlder space associatedwith the system of vector fields X. |
| doi_str_mv | 10.1007/bf02109387 |
| format | Article |
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We have provedthe existence and the maximal regularity of solutions in the &quot;non-isotropic&quot; Hlder space associatedwith the system of vector fields X.</description><identifier>ISSN: 1439-8516</identifier><identifier>EISSN: 1439-7617</identifier><identifier>DOI: 10.1007/bf02109387</identifier><language>eng</language><subject>equation;Dirichlet ; estimate ; priori ; problem;A ; Sub-elliptic</subject><ispartof>Acta mathematica Sinica. 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English series</title><addtitle>Acta Mathematica Sinica</addtitle><description>&lt;正&gt; In this paper, we study the Dirichlet problems for the following quasilinear secondorder sub-elliptic equation, sum from i,j=1 to m(Xi*(Ai,j（x,u）Xj u)+sum from j=1 to m(Bj（x,u）Xj u+C（x,u）=0 in Ω, u=φ on Ω,where X={X1, …, Xm} is a system of real smooth vector fields which satisfies the Hrmander’scondition, A（i,j）, Bj, C∈C∞（■×R） and (Ai,j（x, z）) is a positive definite matris. We have provedthe existence and the maximal regularity of solutions in the &quot;non-isotropic&quot; Hlder space associatedwith the system of vector fields X.</description><subject>equation;Dirichlet</subject><subject>estimate</subject><subject>priori</subject><subject>problem;A</subject><subject>Sub-elliptic</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1996</creationdate><recordtype>article</recordtype><recordid>eNo9kMFOwzAQRC0EEqVw4Qt8BgXWTmzHRygtVKpUEHCObHfdGqVJaycH_p5UFE6zIz2NZoeQawZ3DEDdWw-cgc5LdUJGrMh1piRTp8e7FEyek4uUvgCE0CBHZP4UYnCbGjv6Gltb4zZR30babZC-9SaFOjRoIn1H1zYruowrHExvsa7DrguOTve96ULbpEty5k2d8OqoY_I5m35MXrLF8nk-eVhkjgvoMlVYVKi5KwVyhsoPVbwXshDWlYZLXxRWm6GodM5pXDnLuRqeKtFDAcDzMbn5zXWxTSmir3YxbE38rhhUhxGqx9nfCAN8e4Q3bbPeh2b9T0sppFKqzJnWEtgh-gfOB1xb</recordid><startdate>1996</startdate><enddate>1996</enddate><creator>Chaojiang, Xu</creator><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>W94</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>1996</creationdate><title>Dirichlet Problems for the Quasilinear Second Order Subelliptic Equations</title><author>Chaojiang, Xu</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c250t-74be7e92c85e21e7f005ff5645bc8a26f44b9a5166ccc9edcb2270218ef040023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1996</creationdate><topic>equation;Dirichlet</topic><topic>estimate</topic><topic>priori</topic><topic>problem;A</topic><topic>Sub-elliptic</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chaojiang, Xu</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库-自然科学</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><jtitle>Acta mathematica Sinica. 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We have provedthe existence and the maximal regularity of solutions in the &quot;non-isotropic&quot; Hlder space associatedwith the system of vector fields X.</abstract><doi>10.1007/bf02109387</doi><tpages>15</tpages></addata></record> |
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| ispartof | Acta mathematica Sinica. English series, 1996, Vol.12 (1), p.18-32 |
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| source | SpringerNature Journals; Alma/SFX Local Collection |
| subjects | equation Dirichlet estimate priori problem A Sub-elliptic |
| title | Dirichlet Problems for the Quasilinear Second Order Subelliptic Equations |
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