Accepted Paper

Inserted: 31 jul 2026
Last Updated: 31 jul 2026

Journal: Advances in Calculus of Variations
Volume: 13
Number: (3)
Pages: 279-300
Year: 2020
Doi: 10.1515/acv-2017-0037

Abstract:

Integrals of the Calculus of Variations with $p,q$-growth may have not smooth minimizers, not even bounded, for general $p,q$ exponents. In this paper we consider the scalar case, which contrary to the vector-valued one, allows us not to impose structure conditions on the integrand $f(x,\xi)$ with dependence on the modulus of the gradient i.e. $f(x,\xi)=g(x,
\xi
)$. Without imposing structure conditions, we prove that if $\frac{q}{p}$ is sufficiently close to $1$ then every minimizer is locally Lipschitz-continuous.

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