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Regularity for minimizers of a class of non-autonomous functionals with sub-quadratic growth
Advances in Calculus of Variations ( IF 1.3 ) Pub Date : 2020-03-19 , DOI: 10.1515/acv-2019-0092
Andrea Gentile 1
Affiliation  

We consider a class of integral functionals with convex integrand with respect to the gradient variable, assuming that the function that measures the oscillation of the integrand with respect to the x variable belongs to a suitable Sobolev space W^{1;q}. We prove a result of higer differentiability for the minimizers. We also infer a result of Lipschitz regularity of minimizers if q > n, and a result of higher integrability for the gradient if q = n. The novelty here is that we deal with integrands satisfying subquadratic growth conditions with respect to gradient variable.

中文翻译:

一类具有次二次增长的非自治泛函的极小值的正则性

我们考虑一类关于梯度变量具有凸被积函数的积分函数,假设测量被积函数相对于 x 变量的振荡的函数属于合适的 Sobolev 空间 W^{1;q}。我们证明了最小化器的更高可微性的结果。如果 q > n,我们还推断出极小值的 Lipschitz 正则性的结果,如果 q = n,则推断出梯度具有更高的可积分性。这里的新颖之处在于我们处理满足关于梯度变量的次二次增长条件的被积函数。
更新日期:2020-03-19
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