Gradient regularity for non-autonomous functionals with Dini or non-Dini continuous coefficients

Date

2022-11-23

Authors

Baroni, Paolo
Coscia, Alessandra

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We prove C1 regularity for local vectorial minimizers of the non-autonomous functional w ∈ W1,1 loc (Ω; ℝN) ↦ ∫Ω b(x)[|Dw|p log(e + |Dw|)]dx, with Ω open subset of Rn, n≥2 , p>1, 0≤a(.)≤
a
L∞(Ω)<∞, and 0<ν≤b(.)≤ L. The result is valid provided that the function a(.) is log-Dini continuous and that the coefficient b(.) is Dini continuous or it is weakly differentiable and its gradient locally belongs to the Lorentz space Ln,1(Ω;Rn).

Description

Keywords

non-autonomous functionals, gradient continuity, dini continuous coefficients

Citation

Baroni, P., & Coscia, A. (2022). Gradient regularity for non-autonomous functionals with Dini or non-Dini continuous coefficients. <i>Electronic Journal of Differential Equations, 2022</i>(80), pp. 1-30.

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Attribution 4.0 International

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