当前位置: X-MOL 学术Adv. Calc. Var. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Regularity for scalar integrals without structure conditions
Advances in Calculus of Variations ( IF 1.3 ) Pub Date : 2020-07-01 , DOI: 10.1515/acv-2017-0037
Michela Eleuteri 1 , Paolo Marcellini 2 , Elvira Mascolo 2
Affiliation  

Abstract Integrals of the Calculus of Variations with p , q {p,q} -growth may have not smooth minimizers, not even bounded, for general p , q {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 , ξ ) {f(x,\xi)} with dependence on the modulus of the gradient, i.e. f ⁢ ( x , ξ ) = g ⁢ ( x , | ξ | ) {f(x,\xi)=g(x,|\xi|)} . Without imposing structure conditions, we prove that if q p {\frac{q}{p}} is sufficiently close to 1, then every minimizer is locally Lipschitz-continuous.

中文翻译:

无结构条件的标量积分的正则性

对于一般的 p , q {p,q} 指数,具有 p , q {p,q} -growth 的变分积分的抽象积分可能没有平滑的极小值,甚至没有界。在本文中,我们考虑标量情况,与矢量值相反,它允许我们不将结构条件强加给被积函数 f ⁢ ( x , ξ ) {f(x,\xi)} 依赖于梯度,即 f ⁢ ( x , ξ ) = g ⁢ ( x , | ξ | ) {f(x,\xi)=g(x,|\xi|)} 。在不施加结构条件的情况下,我们证明如果 qp {\frac{q}{p}} 足够接近 1,那么每个极小值都是局部 Lipschitz 连续的。
更新日期:2020-07-01
down
wechat
bug