Global integrability for weak solutions to some anisotropic elliptic equations. (January 2015)

• Record Type: Journal Article
• Authors: Innamorati, Alessandra; Leonetti, Francesco
• Is Part Of: Nonlinear analysis. Volume 113(2015)
• Page Start: 430
• Page End: 434
• Publication Date: 2015-01
• Subjects: 35J60 -- 35D30 -- 35J25 -- 49N60; Integrability -- Solution -- Anisotropic -- Elliptic -- Equation; 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.2014.09.027
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the boundary value problem { ∑ i = 1 n D i ( a i ( x, D u ( x ) ) ) = 0, x ∈ Ω ; u ( x ) = u ∗ ( x ), x ∈ ∂ Ω . We show that higher integrability of the boundary datum u ∗ forces solutions u to have higher integrability as well. Assumptions on a i ( x, z ) are suggested by Euler equation of the anisotropic functional ∫ Ω ∑ i = 1 n ( 2 | D i u | 2 + | D i u | sin ( | D i u | ) ) p i 2 .