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




Harjulehto, Petteri; Hästö, Peter; Torricelli, Andrea

PublisherAmerican Institute of Mathematical Sciences (AIMS)

SPRINGFIELD

2025

Communications on Pure and Applied Analysis

Communications on Pure and Applied Analysis

COMMUN PUR APPL ANAL

24

9

1615

1626

12

1534-0392

1553-5258

DOIhttps://doi.org/10.3934/cpaa.2025051

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



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.



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) .


Last updated on 2025-06-05 at 10:42