Higher integrability for anisotropic parabolic systems of p-Laplace type - Mons, Léon (Advances in Nonlinear Analysis, 2023)
In this article, we consider anisotropic parabolic systems of p p -Laplace type. The model case is the parabolic p i -Laplace system u t - i = 1 n x i (D i u p i - 2 D i u) = 0 =0 with exponents p i ≥ 2. Under the assumption that the exponents are not too far apart, i.e., the difference p max - p min p_-p_ is sufficiently small, we establish a higher integrability result for weak solutions. This extends a result, which was only known for the elliptic setting, to the parabolic setting.
CRIS-Team Scopus Importer:2023-05-26
Keywords: finite differences; higher integrability; parabolic systems

Higher regularity for minimizers of very degenerate integral functionals - Mons, Léon (Journal of Mathematical Analysis and Applications, 2023)
In this article, we consider minimizers of integral functionals of the type [Formula presented] with a bounded domain Ω⊂Rn(n≥2), a growth exponent p≥2 and Lipschitz continuous coefficients a:Ω→R. We consider the vectorial setting, i.e. u:Ω→RN with N≥1. We will prove that H(Du) is continuous for any continuous function H:RNn→R vanishing on ξ∈RNn:|ξ|≤1. This extends a recent result from [3] to the case of integrands that explicitly depend on the x-variable.
CRIS-Team Scopus Importer:2024-12-16
Keywords: Asymptotically convex functionals; C; Degenerate elliptic systems

PARTIAL REGULARITY FOR PARABOLIC SYSTEMS WITH VMO-COEFFICIENTS - Mons, Léon (Communications on Pure and Applied Analysis, 2021)
In this article we establish a partial Holder continuity result for weak solutions of parabolic systems, where the nonlinear vector field A(.) satisfies a standard p-growth condition and a non-degenerate ellipticity condition with respect to the gradient variable, while in the space-time variable z = (x, t) it verifies a VMO-type condition. Thus, no continuity in the space-time variable is assumed. The proof is based on the method of A-caloric approximation, applied on suitably chosen intrinsic cylinders.
CRIS-Team WoS Importer:2021-05-28