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Zeitschrift für Analysis und ihre Anwendungen


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Volume 38, Issue 3, 2019, pp. 329–349
DOI: 10.4171/ZAA/1640

Published online: 2019-07-15

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

Josef Daněček[1] and Eugen Viszus[2]

(1) Technical University of Ostrava, Czech Republic
(2) Comenius University, Bratislava, Slovakia

We consider minima of variational integrals with non-differentiable integrands in the form $f(x,u,Du)= \langle A(x)Du,Du\rangle+g(x,u,Du)$. 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.

Keywords: Nonlinear functionals, regularity, Morrey–Campanato spaces

Daněček Josef, Viszus Eugen: On Morrey and BMO Regularity for Gradients of Minima of Certain Non-Differentiable Functionals. Z. Anal. Anwend. 38 (2019), 329-349. doi: 10.4171/ZAA/1640