Lipschitz estimates for systems with ellipticity conditions at infinity

被引:81
作者
Eleuteri, Michela [1 ]
Marcellini, Paolo [1 ]
Mascolo, Elvira [1 ]
机构
[1] Univ Florence, Dipartimento Matemat & Informat U Dini, Viale Morgagni 67-A, I-50134 Florence, Italy
关键词
Elliptic systems; Local minimizers; Local Lipschitz continuity; p; q-growth; Variable exponents; EVERYWHERE-REGULARITY; MINIMIZERS; FUNCTIONALS; EXISTENCE; INTEGRALS; EQUATIONS; CALCULUS;
D O I
10.1007/s10231-015-0529-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 integral(Omega) g(x, vertical bar Du vertical bar) dx, with p, q-growth conditions only for vertical bar Du vertical bar -> +infinity and without further structure conditions on the integrand g = g( x, vertical bar Du vertical bar). We apply the regularity results to weak solutions to nonlinear elliptic systems of the form Sigma(n)(i=1) partial derivative/partial derivative x(i) a(i)(alpha) (x, Du) = 0, alpha = 1, 2, . . . , N.
引用
收藏
页码:1575 / 1603
页数:29
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