一类具低阶项和退化强制的椭圆方程的有界弱解

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 529-534.

一类具低阶项和退化强制的椭圆方程的有界弱解

李仲庆^1,*(),高文杰²

¹ 贵州财经大学数统学院贵阳 550025
² 吉林大学数学学院长春 130012

收稿日期:2017-12-15 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 李仲庆 E-mail:jlu@163.com
基金资助:
国家自然科学基金(11401252);贵州财经大学引进人才科研启动基金(2018YJ26)

Bounded Weak Solutions to an Elliptic Equation with Lower Order Terms and Degenerate Coercivity

Zhongqing Li^1,*(),Wenjie Gao²

¹ School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025
² School of Mathematics, Jilin University, Changchun 130012

Received:2017-12-15 Online:2019-06-26 Published:2019-06-27
Contact: Zhongqing Li E-mail:jlu@163.com
Supported by:
the NSFC(11401252);the Scientific Research Foundation for the Introduction of Talent in GUFE(2018YJ26)

摘要/Abstract

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.

关键词: 椭圆方程, 退化强制, 低阶项, L^∞正则性

Abstract:

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.

Key words: Elliptic equations, Degenerate coercivity, Lower order terms, L^∞ regularity

中图分类号:

O175.8

李仲庆,高文杰. 一类具低阶项和退化强制的椭圆方程的有界弱解[J]. 数学物理学报, 2019, 39(3): 529-534.

Zhongqing Li,Wenjie Gao. Bounded Weak Solutions to an Elliptic Equation with Lower Order Terms and Degenerate Coercivity[J]. Acta mathematica scientia,Series A, 2019, 39(3): 529-534.

参考文献 8

1	Boccardo L , Brezis H . Some remarks on a class of elliptic equations with degenerate coercivity. Boll Unione Mat Ital Sez B Artic 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 Léon 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- 713
	Gao 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 Inequalities and Their Applications. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 2000

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