Calculus of Variations and Geometric Measure Theory

G. Cupini - R. Petti

Morrey spaces and local regularity of minimizers of variational integrals

created on 22 Dec 2001
modified on 13 Jan 2003


Published Paper

Inserted: 22 dec 2001
Last Updated: 13 jan 2003

Journal: Rend. Mat. Appl
Volume: 21
Pages: 121-141
Year: 2001


We study the regularity (Hölder continuity, $BMO$, higher summability) of local minimizers of integral functionals of the Calculus of Variations in the scalar case. We assume that the integrand satisfies a growth condition involving a function which belongs to a certain Morrey space. No differentiability assumption is required. Analogous results are proved for weak solutions of nonlinear elliptic equations of $p$-Laplacian type.

Keywords: regularity, Local minimizers, Morrey spaces