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