Hölder estimates for the elliptic p(x)-Laplacian equation with the logarithmic function. Issue 8 (24th May 2022)

• Record Type: Journal Article
• Authors: Yao, Fengping
• Is Part Of: Applicable analysis. Volume 101:Issue 8(2022)
• Page Start: 3048
• Page End: 3064
• Publication Date: 2022-05-24
• Subjects: C1α -- Hölder -- gradient -- regularity -- divergence -- elliptic -- p(x)-Laplacian -- logarithmic; 35J60 -- 35J70; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1836348
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper we obtain the interior Hölder regularity of the gradient for the elliptic p ( x ) -Laplacian equation with the logarithmic function 1 d i v A ∇ u ⋅ ∇ u p ( x ) − 2 2 ln e + A ∇ u ⋅ ∇ u 1 / 2 A ∇ u = d i v | f | p ( x ) − 2 ln e + f f under some proper assumptions on the Hölder continuous functions p, f and A . This extends previous results obtained by Giannetti and Passarelli di Napoli [Regularity results for a new class of functionals with non-standard growth conditions. J. Differ Equ. 2013;254(3):1280–1305], where A is the identity matrix and hence does not depend on x .