Higher differentiability of minimizers of variational integrals with Sobolev coefficients

被引:57
作者
di Napoli, Antonia Passarelli [1 ]
机构
[1] Univ Naples Federico II, Dipartimento Mat & Appl R Caccioppoli, I-80126 Naples, Italy
关键词
Degenerate functionals; regularity of minimizers; PARTIAL REGULARITY; HIGHER INTEGRABILITY; MAXIMUM PRINCIPLE; EQUATIONS; FUNCTIONALS; CONTINUITY; CALCULUS;
D O I
10.1515/acv-2012-0006
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we consider integral functionals of the form F(nu, Omega) = integral(Omega) F(x, D nu(x)) dx with convex integrand satisfying p growth conditions with respect to the gradient variable. As a novel feature, the dependence of the integrand on the x-variable is allowed to be through a Sobolev function. We prove local higher differentiability results for local minimizers of the functional F, establishing uniform higher differentiability estimates for solutions to a class of auxiliary problems, constructed adding singular higher order perturbations to the integrand. Furthermore, we prove a dimension free higher integrability result for the gradient of local minimizers, by the use of a weighted version of the Gagliardo-Nirenberg interpolation inequality.
引用
收藏
页码:59 / 89
页数:31
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