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Regularity under nonstandard growth conditions

  • Emilio Acerbi (Parma)
A3 01 (Sophus-Lie room)

Abstract

Some regularity results are presented for local minimizers of integral functionals $$\int f (x,Du)dx$$ satisfying non standard growth assumptions, i.e., such that the growth exponent $q$ and the ellipticity exponent $p$ are different in the inequality $$|z|^p \leq f (x,z) \leq 1 + |z|^q$$ Both the homogeneous-anisotropic and the inhomogeneous-isotropic cases are considered.

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