Calculus of Variations and Geometric Measure Theory
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L. Esposito - F. Leonetti - G. Mingione

Higher integrability for minimizers of integral functionals with $(p,q)$ growth.

created on 01 Feb 2002
modified on 06 Jul 2002

[BibTeX]

Published Paper

Inserted: 1 feb 2002
Last Updated: 6 jul 2002

Journal: J. Differential Equations
Volume: 157
Number: 2
Pages: 414-438
Year: 1999

Abstract:

We consider functionals of the type $$ \int f(Du) +a(x)u$$ defined on vector values functions $u:\Omega \to R^N$, where $f$ satisfies growth conditions of $(p,q)$ type: $$ L{-1}
z
p \leq f(z) \leq L(1+
z
q).$$ Moreover $f$ is convex and satisfies the natural growth and ellipticity assumptions on the matrix $D^2f$. We prove local $W^{1,q}$ regularity of minimizers provided $$ qp < (n+2)n$$ where $\Omega \subset R^n$. A higher differentiability result is also given.

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