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

References in corpus (5)

• Regularity for double phase problems at nearly linear growth
• Partial Regularity for BV Minimizers
• Regularity theory for non-autonomous partial differential equations without Uhlenbeck structure
• A fundamental condition for harmonic analysis in anisotropic generalized Orlicz spaces
• Global geometry and $C^1$ convex extensions of $1$-jets