On Morrey and BMO Regularity for Gradients of Minima of Certain Non-Differentiable Functionals

Josef Daněček; Eugen Viszus

doi:10.4171/zaa/1640

JournalszaaVol. 38, No. 3pp. 329–349

On Morrey and BMO Regularity for Gradients of Minima of Certain Non-Differentiable Functionals

Josef Daněček
Technical University of Ostrava, Czech Republic
Eugen Viszus
Comenius University, Bratislava, Slovakia

A subscription is required to access this article.

Abstract

We consider minima of variational integrals with non-differentiable integrands in the form $f (x, u, D u) = ⟨ A (x) D u, D u ⟩ + g (x, u, D u)$ . Assuming that the part $g (x, u, z)$ is equipped by sub-quadratic growth in $z$ only for big value of $∣ z ∣$ (but the growth is arbitrarily close to the quadratic one), we prove the everywhere Morrey and BMO regularity for gradients of minima.

Cite this article

Josef Daněček, Eugen Viszus, On Morrey and BMO Regularity for Gradients of Minima of Certain Non-Differentiable Functionals. Z. Anal. Anwend. 38 (2019), no. 3, pp. 329–349

DOI 10.4171/ZAA/1640