Higher differentiability of minimizers for non-autonomous orthotropic functionals

IF 1.8 3区 数学 Q1 MATHEMATICS, APPLIED
Stefania Russo
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引用次数: 0

Abstract

We establish the higher differentiability for the minimizers of the following non-autonomous integral functionals F(u,Ω)Ωi=1nai(x)|uxi|pidx,with exponents pi2 and with coefficients ai(x) that satisfy a suitable Sobolev regularity. The main result is obtained, as usual, by imposing a gap bound on the exponents pi, which depends on the dimension and on the degree of regularity of the coefficients ai(x).
非自治正交各向异性泛函的高可微性
我们建立了下列非自治积分泛函数F(u,Ω)在指数pi≥2和系数ai(x)满足适当的Sobolev正则性的条件下,对∑i=1nai(x)|uxi|pidx的最小值的高可微性。像往常一样,主要结果是通过在指数pi上施加间隙界得到的,该间隙界取决于系数ai(x)的维数和规则程度。
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来源期刊
CiteScore
3.80
自引率
5.00%
发文量
176
审稿时长
59 days
期刊介绍: Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.
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