一类具低阶项和退化强制的椭圆方程的有界弱解
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摘要
该文研究了一类具低阶项和退化强制的椭圆方程的边值问题.借助于De Giorgi迭代技术和Boccardo-Brezis的检验函数,得到了解的L~∞估计.利用L~∞界证明了方程解的存在性.
A boundary value problem to a class of elliptic equations with lower order terms and degenerate coercivity is studied in this paper.With help of De Giorgi iterative technique and Boccardo-Brezis' s test function,the L~∞ estimate to weak solutions of the problem is obtained.Based upon the uniform L~∞ bound,the existence of bounded solution is proved.
A boundary value problem to a class of elliptic equations with lower order terms and degenerate coercivity is studied in this paper.With help of De Giorgi iterative technique and Boccardo-Brezis' s test function,the L~∞ estimate to weak solutions of the problem is obtained.Based upon the uniform L~∞ bound,the existence of bounded solution is proved.
引文
[1]Boccardo L,Brezis H.Some remarks on a class of elliptic equations with degenerate coercivity.Boll Unione Mat Ital Sez B Artie Ric Mat,2003,6(3):521-530
[2]Boccardo L,Dall'Aglio A,Orsina L.Existence and regularity results for some elliptic equations with degenerate coercivity.Atti Sem Mat Fis Univ Modena,1998,46(supp 1):51-81
[3]Boccardo L,Murat F,Puel J P.L~∞estimate for some nonlinear elliptic partial differential equations and application to an existence result.SIAM J Math Anal,1992,23(2):326-333
[4]Boccardo L,Segura de Le6n S,Trombetti C.Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic gradient term.J Math Pures Appl,2001,80(9):919-940
[5]Boccardo L,Croce G.Elliptic Partial Differential Equations:Existence and Regularity of Distributional Solutions.Berlin:De Gruyter,2014
[6]高红亚,贾苗苗.障碍问题解的局部正则性和局部有界性.数学物理学报,2017,37A(4):706-713Gao H Y,Jia M M.Local regularity and local boundedness for solutions to obstacle problems.Acta Math Sci,2017,37A(4):706-713
[7]Zeidler E.Nonlinear Functional Analysis and Its Applications II/B:Nonlinear Monotone Operators.New York:Springer-Verlag,1990
[8]Kinderlehrer D,Stampacchia G.An Introduction to Variational Inequailities and Their Applications.Philadelphia,PA:Society for Industrial and Applied Mathematics(SIAM),2000
[2]Boccardo L,Dall'Aglio A,Orsina L.Existence and regularity results for some elliptic equations with degenerate coercivity.Atti Sem Mat Fis Univ Modena,1998,46(supp 1):51-81
[3]Boccardo L,Murat F,Puel J P.L~∞estimate for some nonlinear elliptic partial differential equations and application to an existence result.SIAM J Math Anal,1992,23(2):326-333
[4]Boccardo L,Segura de Le6n S,Trombetti C.Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic gradient term.J Math Pures Appl,2001,80(9):919-940
[5]Boccardo L,Croce G.Elliptic Partial Differential Equations:Existence and Regularity of Distributional Solutions.Berlin:De Gruyter,2014
[6]高红亚,贾苗苗.障碍问题解的局部正则性和局部有界性.数学物理学报,2017,37A(4):706-713Gao H Y,Jia M M.Local regularity and local boundedness for solutions to obstacle problems.Acta Math Sci,2017,37A(4):706-713
[7]Zeidler E.Nonlinear Functional Analysis and Its Applications II/B:Nonlinear Monotone Operators.New York:Springer-Verlag,1990
[8]Kinderlehrer D,Stampacchia G.An Introduction to Variational Inequailities and Their Applications.Philadelphia,PA:Society for Industrial and Applied Mathematics(SIAM),2000