Baroni, PaoloCoscia, Alessandra2023-05-152023-05-152022-11-23Baroni, 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. 1-30.1072-6691https://hdl.handle.net/10877/16804We 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(.)≤aL∞(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).Text30 pages1 file (.pdf)enAttribution 4.0 Internationalnon-autonomous functionalsgradient continuitydini continuous coefficientsArticle