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

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 $C^1$-energies.

The first word in the title was "monotonic" in earlier versions of the manuscript