Monotone approximation of differentiable convex functions with applications to general minimization problems - UTU Research Portal

A1 Refereed original research article in a scientific journal

Monotone approximation of differentiable convex functions with applications to general minimization problems

Authors: Harjulehto, Petteri; Hästö, Peter; Torricelli, Andrea

Publisher: American Institute of Mathematical Sciences (AIMS)

Publishing place: SPRINGFIELD

Publication year: 2025

Journal: Communications on Pure and Applied Analysis

Journal name in source: Communications on Pure and Applied Analysis

Journal acronym: COMMUN PUR APPL ANAL

Volume: 24

Issue: 9

First page : 1615

Last page: 1626

Number of pages: 12

ISSN: 1534-0392

eISSN: 1553-5258

DOI: https://doi.org/10.3934/cpaa.2025051

Web address : https://doi.org/10.3934/cpaa.2025051

Abstract

We study minimizers of non-autonomous energies with minimal growth and coercivity assumptions on the energy. We show that the minimizer is nevertheless the solution of the relevant Euler-Lagrange equation or inequality. The main tool is an extension result for convex C1-energies.

Funding information in the publication:
The author has been partially supported through the INdAM-GNAMPA 2024 Project "Inter-azione ottimale tra la regolarita dei coefficienti e l'anisotropia del problema in funzionali integrali a crescite non standard" (CUP: E53C23001670001) .