Interior gradient regularity for BV minimizers of singular variational problems. (June 2015)

• Record Type: Journal Article
• Authors: Beck, Lisa; Schmidt, Thomas
• Is Part Of: Nonlinear analysis. Volume 120(2015)
• Page Start: 86
• Page End: 106
• Publication Date: 2015-06
• Subjects: 49N60 -- 35J75 -- 26B30; Generalized minimizers -- Functions of bounded variation -- Singular elliptic problems -- Regularity; 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.2015.02.011
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider a class of vectorial integrals with linear growth, where, as a key feature, some degenerate/singular behavior is allowed. For generalized minimizers of these integrals in BV, we establish interior gradient regularity and–as a consequence–uniqueness up to constants. In particular, these results apply, for 1 < p < 2, to the singular model integrals ∫ Ω ( 1 + | ∇ w ( x ) | p ) 1 p d x .