Work

Regularity results for minimizers of non-autonomous integral functionals

Year: 2025

Type: article

Abstract: We establish the higher fractional differentiability for the minimizers of non-autonomous integral functionals of the form \begin{align*} \mathcal{F}(u,\Omega):=\int_\Omega \left[ f(x,Du)- g \cdot u \right] dx , \end{align*} under (p, q)-growth conditions. Besides a suitable differentiability assumption on the partial map $x \mapsto D_\xi f(x,\xi)$ , we do not need to assume any differentiability assumption on the function g.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2025.10039

Authors: Antonio Giuseppe Grimaldi, Stefania Russo

Institutions: Parthenope University of Naples, University of Naples Federico II

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Ministero dell'Università e della Ricerca