Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 95-103

BOUNDED VERY WEAK SOLUTIONS FOR SOME NON-UNIFORMLY ELLIPTIC EQUATION WITH L¹ DATUM

Chao Zhang and Shulin Zhou

Harbin Institute of Technology, Department of Mathematics
Harbin 150001, P.R. China; czhangmath 'at' hit.edu.cn

Peking University, LMAM, School of Mathematical Sciences
Beijing 100871, P.R. China; szhou 'at' math.pku.edu.cn

Abstract. In this paper we obtain the existence of bounded very weak solutions for the Dirichlet boundary value problem of a class of non-uniformly elliptic equations with L¹ integrability conditions by using the regularizing effect of the interaction between the coefficient of lower order term and the datum in the right-hand side.

2010 Mathematics Subject Classification: Primary 35D05; Secondary 35D10.

Key words: Very weak solutions, existence, elliptic, non-uniformly, L¹ datum.

Reference to this article: C. Zhang and S. Zhou: Bounded very weak solutions for some non-uniformly elliptic equation with L¹ datum. Ann. Acad. Sci. Fenn. Math. 42 (2017), 95-103.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4205

BOUNDED VERY WEAK SOLUTIONS FOR SOME NON-UNIFORMLY ELLIPTIC EQUATION WITH L1 DATUM

Chao Zhang and Shulin Zhou

BOUNDED VERY WEAK SOLUTIONS FOR SOME NON-UNIFORMLY ELLIPTIC EQUATION WITH L¹ DATUM