Some Results on Evolutionary Equations Involving Functions of the Curvatures of the Graph

51.Introducti0nandMainResultlnthepaperL1J,Caffarelli,NirenbergandSpruckdiscussedtheDirichletproblemforthenonlinearellipticequationforunknownu=u(x):{':<;;>:,<";>:are,vxeD,(1-1)where0lsab0undedstrictlyconvexdomaininR"withsmoothboundaryare,K(u)=(K,(u),Kz(u),..',K"(u))denotestheprincipalcurvaturesofthegraph(x,u(x))andfisofaspecialnatureasinL2J'L3j.Typicalcasesoftheequationin(1.l),whichweretreatedaswellbyIvochkina[4J,isf=Sl/*(K),whereS*(K)arethee1ementarysymmetricfunctions,Recently,Ivochki…     

二阶椭圆型方程的Александров-Бакельман极值原理

二阶椭圆型方程的极值原理,不仅推广了古典极值原理,而且在解的Holder模估计上也起到了作用(见[22],[32]-[34].不过这类极值原理的陈述和证明,却至少散布在[4]-[9],[11]-[14]这一系列文献中,而且有的文献很难查找,学起     

Some Results on Evolutionary Equations Involving Functions of the Eigenvalues of the Hessian

How to design the parabolic counterpart of the nonlinear elliptic equation involving function of the eigenvalues of the Hessian is discussed and the first initial-boundary value problem for such a parabolic equation is studied.     

Riemann流形上的抛物型Monge-Ampère方程

This paper deals with a class of parabolic Monge-Ampère equation on Riemannian manifolds. The existence and uniqueness of the solution to the first initial-boundary value problem for the equation are established.     

Some Remarks on One Type of Parabolic Monge-Ampère Equation

Inthepresentpaper,weinvestigatethefollowinginitial--boundaryvalueproblemforatypeofparabolicMonge-AmpereequationwhereQ=ax(0,TI,nisaboundedconvexdomaininR",aamistheHessianofthefunctionu,ovQdenotestheparabolicboundaryofQ.Recently,IvochkinaandLadyzhenskaya[1]consideredtheaboveproblem,andundersomestructureconditions,theyobtainedtheuniquesolvabilityofitinclassicalsense.Afterthat,WangRouhuaiandWangGuanglieimprovedtheresultsof[ifundersomeweakerconditionsandgetthatproblem(1),(2)hasauniquesolution…     

关于一类抛物型Monge-Ampère方程解的注记

本文讨论如下抛物型Monge-Ampere方程的第一初边值问题-ut+det1/nD2u=g(x,t),(x,t)∈Q=Ω×(0,T],u=ψ(z,t),(z,t)∈apQ,其中Ω为Rn中有界凸集.证明了在更一般的结构条件下[3,7]的结果仍然成立.证明中重要的一点是在Rn×R中非柱型域上"冻结问题"的可解性.