In the general vector-valued case N≥ 1 , we prove the Lipschitz continuity of local minimizers to some integrals of the calculus of variations of the form ∫Ωg(x,|Du|)dx, with p, q-growth conditions only for | Du| → + ∞ and without further structure conditions on the integrand g= g(x, | Du|). We apply the regularity results to weak solutions to nonlinear elliptic systems of the form ∑i=1n∂∂xiaiα(x,Du)=0, α= 1 , 2 , … , N.
Lipschitz estimates for systems with ellipticity conditions at infinity / Eleuteri, Michela; Marcellini, Paolo; Mascolo, Elvira. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 195:5(2016), pp. 1575-1603. [10.1007/s10231-015-0529-4]
Lipschitz estimates for systems with ellipticity conditions at infinity
ELEUTERI, Michela;
2016
Abstract
In the general vector-valued case N≥ 1 , we prove the Lipschitz continuity of local minimizers to some integrals of the calculus of variations of the form ∫Ωg(x,|Du|)dx, with p, q-growth conditions only for | Du| → + ∞ and without further structure conditions on the integrand g= g(x, | Du|). We apply the regularity results to weak solutions to nonlinear elliptic systems of the form ∑i=1n∂∂xiaiα(x,Du)=0, α= 1 , 2 , … , N.
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