Absence of Lavrentiev gap for non-autonomous functionals with (p, q)-growth

被引：26

作者：

Esposito, Antonio ^{[1
]}

Leonetti, Francesco ^{[1
]}

Petricca, Pier Vincenzo ^{[1
]}

机构：

[1] Univ Aquila, DIS, Via Vetoio Snc, I-67100 Laquila, Italy

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2019年 / 8卷 / 01期

关键词：

Variational integrals; non-standard growth; regularity; Lavrentiev gap; MINIMIZERS; REGULARITY; INTEGRALS;

D O I：

10.1515/anona-2016-0198

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider non-autonomous functionals of the form F(u, Omega) =integral(Omega) f(x, Du(x))dx, where u : Omega -> R-N, Omega subset of R-n. We assume that f(x, z) grows at least as vertical bar z vertical bar(p) and at most as vertical bar z vertical bar(q). Moreover, f(x, z) is Holder continuous with respect to x and convex with respect to z. In this setting, we give a sufficient condition on the density f(x, z) that ensures the absence of a Lavrentiev gap.

引用

页码：73 / 78

页数：6

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