MAXIMUM PRINCIPLES FOR GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (4): 458-467.

MAXIMUM PRINCIPLES FOR GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

王向东, 徐小增, 梁(汲金)廷

Faculty of Sciences, Foshan University of Science and Technology, Foshan, Guangdong 528000, P. R. China

收稿日期:2002-12-18 修回日期:2002-11-19 出版日期:2003-04-18 发布日期:2003-04-18

MAXIMUM PRINCIPLES FOR GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

WANG Xiang-dong, XU Xiao-zeng, LIANG Xi-ting

Faculty of Sciences, Foshan University of Science and Technology, Foshan, Guangdong 528000, P. R. China

Received:2002-12-18 Revised:2002-11-19 Online:2003-04-18 Published:2003-04-18

摘要/Abstract

摘要： Under the assumption that the growth order of the free term to satisfy the natural growth condition with respect to gradient of the generalized solutions, the maximum principle is proved for the bounded generalized solution of quasi-linear elliptic equations.

中图分类号:

王向东;徐小增;梁(汲金)廷. MAXIMUM PRINCIPLES FOR GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(4): 458-467.

WANG Xiang-dong;XU Xiao-zeng;LIANG Xi-ting . MAXIMUM PRINCIPLES FOR GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(4): 458-467.

参考文献

[1] Ladyzenskaja O A, Ural'ceva N N. Linear and Quasilinear Elliptic Equations [M]. Second Russian Edition, Moscow:Nauka, 1973. (in Russian).
[2] Gilbarg D, Trudinger N S. Elliptic Partial Differential Equations of Second Order [M]. Heidelberg, New York:Springer-Verlag, 1997.
[3] Morry C B. Second order elliptic equations in several variables and Hölder continuity[J]. Math Z, 1959, 72(4):146-164.
[4] Bicadze A B. Some linear questions of linear partial differential equations [J]. Advances in Mathematics, 1958, 4 (3):320-403. (in Chinese).
[5] Trudinger N S. Maximum principles for linear nonuniformly elliptic oprerators with measurable coefficients[J]. Math Z, 1977, 156(4):291-310.
[6] LIANG Xi-ting, YU Ming-qi. The weak maximum principle for gneralized solutions of second-order linear elliptic equations [J]. Journal of Shanxi University (Nat Sci Ed) 1982, 7(2):8-14. (in Chinese).
[7] Uhlenbeck K. Regularity for a class of nonlinear elliptic systems[J]. Acta Math, 1977, 138(2):219-240.
[8] LIANG Xi-ting. Boundedness and integrabity properties for generalized solutions of elliptic equations [J]. Journal of Shanxi University (Nat Sci Ed), 1986, 9 (1):115-130. (in Chinese).
[9] YU Ming-qi, LIANG Xi-ting. The weak maximum principle for generalized solution of quasi-linearelliptic equations [J]. Journal of Shanxi University (Nat Sci Ed) 1989, 12 (3):240-248. (in Chinese).
[10] LIANG Xi-ting. The maximum principle for generalized solutions of quasi-linear elliptic equations[J]. Acta Sci Nat Univ Sunyatsen, 1988, 27 (3):107-122. (in Chinese).
[11] Serrin J. Local behavior of solutions of quasi-linear equation[J]. Acta Math, 1964, 111(5):247-302.
[12] Trudinger N S. On Harnack type inequalities and their applications to quasi-linear elliptic equations[J]. Comm Pure Appl Math, 1967, 20(3):721-747.
[13] Ladyzenskaja O A, Solonnikov V A, Ural'ceva N N. Linear and quasi-linear equations of parabolic type[J]. Transl Math Monographs, 1968, 23(1):90-95.
[14] LIANG Xi-ting, WANG Xiang-dong. A priori estimate for maximum modulus of generalized solutions of quasi-linear elliptic equations[J]. Applied Mathematics and Mechanics (English Edition), 1990, 11(10):941-953.

[1]	朱砾;李秀华;郭兴明. 椭圆型变分不等式的障碍优化控制问题[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(5): 559-570 .
[2]	房少梅;郭柏灵. Initial-boundary value problem of one class of nonlinear Schrödinger equations described in molecular crystals[J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(2): 139-144 .
[3]	耿堤. null[J]. Applied Mathematics and Mechanics (English Edition), 2007, 28(10): 1373-1382 .
[4]	房少梅;郭柏灵. LONG TIME BEHAVIOR FOR SOLUTION OF INITIAL BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEMS WITH MULTIDIMENSIONAL INHOMOGENEOUS GBBM EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2005, 26(6): 716-721 .
[5]	顾永耕;孙文俊. NONTRIVIAL EQUILIBRIUM SOLUTIONS FOR A SEMILINEAR REACTION-DIFFUSION SYSTEM[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(12): 1382-1389.
[6]	张正策;李开泰. STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(8): 929-936.
[7]	房少梅;郭柏灵. EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(6): 673-683.
[8]	李明忠;徐定华. A CLASS OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR THE SECOND-ORDER E₂ CLASS ELLIPTIC SYSTEMS IN GENERAL FORM[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(2): 163-181.
[9]	邵荣;牛欣;沈祖和. EXISTENCE OF SOLUTIONS FOR NONLINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(1): 99-108.
[10]	姚庆六;马勤生. EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR SOME SEMILINEAR ELLIPTIC EQUATIONS IN ANNULUS[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(12): 1452-1457.
[11]	杨作东;陆启韶. BLOW-UP ESTIMATES FOR A NON-NEWTONIAN FILTRATION SYSTEM[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(3): 332-339.
[12]	刘振海. A CLASS OF PARABOLIC HEMIVARIATIONAL INEQUALITIES[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(9): 1045-1052.
[13]	阿拉坦仓;张鸿庆;钟万勰. PSEUDO-DIVISION ALGORITHM FOR MATRIX MULTIVARIABLE POLYNOMIAL AND ITS APPLICATION[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(7): 733-740.
[14]	Nicolae Tarfulea . EXISTENCE OF THE MINIMAL POSITIVE SOLUTION OF SOME NONLINEAR ELLIPTIC SYSTEMS WHEN THE NONLINEARITY IS THE SUM OF A SUBLINEAR AND A SUPERLINEAR TERM[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(3): 283-290.
[15]	冯春华;黄健民. EXISTENCE AND UNIQUENESS OF ALMOST PERIODIC SOLUTION TO A CLASS OF NONAUTONOMOUS SYSTEM[J]. Applied Mathematics and Mechanics (English Edition), 1999, 20(9): 994-998.

MAXIMUM PRINCIPLES FOR GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

MAXIMUM PRINCIPLES FOR GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价