Monotone approximation of differentiable convex functions with applications to general minimization problems
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 $ C^1 $-energies.
Authors
- Petteri Harjulehto (ORCID: https://orcid.org/0000-0003-1931-2066)
- Peter Hästö (ORCID: https://orcid.org/0000-0002-3507-3424)
- Andrea Torricelli (ORCID: https://orcid.org/0000-0002-8612-4076)
Institutions
- Statistics Finland (FI)
- University of Helsinki (FI)
- Politecnico di Torino (IT)
Publication Details
- Journal
- Communications on Pure & Applied Analysis
- Published
- 2025-01-01
- DOI
- https://doi.org/10.3934/cpaa.2025051
- Primary Topic
- Optimization and Variational Analysis
- Type
- article
- Field-Weighted Citation Impact
- 0.00