第l一2期0Jia1snHeoa灵了uf:“Qliuasi一rellipartieaity”CondotinaonsandaPatrtioalfRegulanrt夕宜101erystmsoNonneaPtilD全fferet宝lEquionsSeeodOrd二阶非线性偏微分方程组的“拟椭圆”条件和部分正则性简怀玉(湖南怀化师专)摘要,如果对某久>R勺,O、所有有界开域TcR”、所有矩阵A任M叨和所“有必任C占(T成立*!。,,f,}`2:、J了{T,:(,+D,)。一。::,()d`,我们就称二阶昨线性偏微分方程组(劝“DoA了(Du)=0。,=l落,2,…,N满足2拟椭圆”条件。这个条件远远弱于通常的椭圆条件“2:二些d星竺哪>川引尸;,本文只假定方程组(劝满足u拟椭圆。”条件(不需要椭圆条件)我们用b10wp技巧证明了方程组的部分正则性第19卷第89年10月91一2期HUN湖AN南数学年刊Vol。9N0eo1一2ANN人LSOFMATHEMATICSt198913aQuasi一elliPtieityo,,CosnditioonsandPPaartiatiallRegularityDifferJiafSystemlEqu(HafoNonlinnearrentiationsfSeeoher’dOrderllenHuaiyu(简怀玉)uaihuaTeae5Coge;Hunan)AbsteoreutnoWnaeProearvetrhePartialo”reg一ularityD。ofweaksolution,sof,se一ndeordeerlinsPatialyestemsA了(Du)rea=0d,一l石,2…N,undrth“qui一elliPtieityonditionwhiehsJf。久l2:,1`(JTIT_,;(,+。un,)。,e。“xforSOll”城eN久>0aanadallsmooth,,boNdedoPndomains少`R”,allmatricesA任Mndll(少功〔C后R)1Ite.InPartrodureetiorn15wellaknlsowt,ntshatthetialgulaityofseeondordernonlinearlliPtieParti一ysem(1)haDtuaAdi了(De)=teons,云=le,2un,…tNeesb,eensdexivlyderh”lliPtieityeonditionn、(2)二二共卫三任dA了(P)JP。一石e有拷a>川梦丢n,V首任Mferenees”N;久>oe(CfsGitaquintaIJ【ditsre),whre口任R”,15oPen,boundedandmooh;Whil。一(o,戳)““《a《一`(`《万’15notnhegreaadieenttosmatattrixsfeBautsinsomdoeaPtelisaedisfifyeldshoee(forlliPtiexamPle,linnrlatsie),qutetiongivtoennteotteityteond一eitioby(2)hese,,heusitro15dworhful“weeakenheondition(2)whiehMoreaivatdtWintueethquasi一lliPtiity”eonditinds本文于1988年9月25H收到第一2期0“一”,adieretQionasauo:dtpioaratsialoRSegulariotyr95erf5y,stemsofN2o止11五earPartialDiff匕tialEqanfeeo廿dd(3)forsofeeo、,。,()}`a、s,丁mosA;(A+D,)D,dNe`(,`Penm久>0A”“nadnallaoth,bo,undodomains少仁R”,allmatrieesA=(a蕊)任AsN,dlljs沪任C志(少Rimilarar)ndition(1)15dquttooeonvexeonditions,otrur“eququasi一elliPtii一eonv介”-eityn,,eonnditionin(3)dueeesimiltvahne“unifoC二prmilyIni,etlyjfeasasex,,eoditirotrtroinas[2]byEs,L2汇e;af,etFy:MoN`kRt,15haunifomlysasitlyi一eon“vex(efe228])it15teheetJF(1Pd尸F任C)二tisfiesourquasi一lliPtiity,,eonditionif,inaddition从zeknOnote(2)andfollowingaassumPtioGreen(5)maofryimPly(3)bythewell-Wn1】leanformulandfollowingnmula“,ofef,`A;(A)D功(`)d`一oralloAfre,Taa,abosavteandall(口沪任H孟,,RN)Butthere15afairlyseelassx,mplesforisfyinggu(3)onostsseatisfying(2)(efWedireafZrea;ttionThtereofetherelaritylofytams(1)whiehanttinhishedirereetnnaPPrsoaehesdnevePedk:byoy}esuGirquintaedsMoimila1;(ef〔thaChfVzns〕andts主feareee)do(x`,otWoRnrmth,od15,toto;Eva2〕〔NottioBr)`{今任5}1den一:【
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