Gradient regularity for non-autonomous functionals with Dini or non-Dini continuous coefficients
Date
2022-11-23
Authors
Baroni, Paolo
Coscia, Alessandra
Journal Title
Journal ISSN
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).
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.
Rights
Attribution 4.0 International