Journal
ADVANCES IN CALCULUS OF VARIATIONS
Volume 13, Issue 3, Pages 279-300Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/acv-2017-0037
Keywords
Elliptic equations; local minimizers; local Lipschitz continuity; p, q-growth; general growth conditions
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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, vertical bar xi vertical bar). Without imposing structure conditions, we prove that if q/p is sufficiently close to 1, then every minimizer is locally Lipschitz-continuous.
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