High regularity of the solution to the singular elliptic p(⋅)-Laplacian system. (January 2020)

• Record Type: Journal Article
• Authors: Crispo, Francesca; Grisanti, Carlo R.
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 35B65 -- 35J55 -- 35Q35; p(x)-Laplacian system -- Higher integrability -- Global regularity -- Variable exponents spaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111603
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the regularity properties of solutions to the non-homogeneous singular p ( x ) -Laplacian system in a bounded domain of R n . Under suitable restrictions on the range of p ( x ), we construct a W 2, r solution, with r > n, that implies the Hölder continuity of the gradient. Moreover, assuming just p ( x ) ∈ ( 1, 2 ) we prove that the second derivatives belong to L 2 .