Monotone approximation of differentiable convex functions with applications to general minimization problems
: Harjulehto, Petteri; Hästö, Peter; Torricelli, Andrea
Publisher: American 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
DOI: https://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.
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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) .