Continuity of solutions to the G-Laplace equation involving measures

Zhang, Yan and Zheng, Jun: Continuity of solutions to the G-Laplace equation involving measures. Electronic journal of qualitative theory of differential equations 39. pp. 1-10. (2019)

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Abstract

We establish local continuity of solutions to the G-Laplace equation involving measures, i.e., −div � g(|∇u|) |∇u| ∇u where µ is a nonnegative Radon measure satisfying µ(Br(x0)) ≤ Crm for any ball Br(x0) ⊂⊂ Ω with r ≤ 1 and m > n − 1 − δ ≥ 0. The function g is supposed to be nonnegative and C 1 -continuous on [0, +∞), satisfying g(0) = 0 and tg0 (t) g(t) ≤ g0, ∀t > 0 with positive constants δ and g0, which generalizes the structural conditions of Ladyzhenskaya–Ural’tseva for an elliptic operator.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 39
Page Range: pp. 1-10
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.39
Uncontrolled Keywords: Elliptikus differenciáloperátor, Differenciálegyenlet
Additional Information: Bibliogr.: p. 8-10. ; összefoglalás angol nyelven
Date Deposited: 2019. Sep. 27. 13:20
Last Modified: 2019. Sep. 27. 13:20
URI: http://acta.bibl.u-szeged.hu/id/eprint/62117

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