Existence results to a nonlinear p(x)-Laplace equation with degenerate coercivity and zero-order term: renormalized and entropy solutions. Issue 2 (1st February 2016)

• Record Type: Journal Article
• Authors: Li, Zhongqing; Gao, Wenjie
• Is Part Of: Applicable analysis. Volume 95:Issue 2(2016)
• Page Start: 373
• Page End: 389
• Publication Date: 2016-02-01
• Subjects: p(x)-Laplace equation -- lower order term -- L1 datum -- truncation method -- Marcinkiewicz estimates with variable exponent; 35J70 -- 35J60 -- 46E35; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1004321
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : This paper is devoted to the study of a nonlinear elliptic equation with degenerate coercivity, zero-order term and L 1 datum in the setting of variable exponent Sobolev space. The authors obtain the existence of renormalized solution and entropy solution via strong convergence of truncation. They also get some a priori estimates to the solution and the generalized gradient of the solution in the Marcinkiewicz space with variable exponent.