论文标题
Lipschitz的定期变量积分的最小化指数的变异积分量
Lipschitz regularity of minimizers of variational integrals with variable exponents
论文作者
论文摘要
在本文中，我们证明了Lipschitz的规律性，用于\ [\ mathfrak {f}（v，ω）= \int_Ω\！\！ f（x，dv（x））\，dx，\]其中，对于$ {n> 2} $和$ n \ ge 1 $，$ω$，$ω$是$ \ mathbb {r}^n $，$ u \ in w^^{1,1}（1,1,1}（ω，\ mathbb，\ mathbb r} $ f： \ Mathbb {r}^{n \ times n} \ to \ mathbb {r} $满足所谓的可变增长条件。该论文的主要新颖性是，我们在orlicz sobolev设置中为能量密度的设置几乎具有至关重要的规律性，这是$ x $变量的函数。
In this paper we prove the Lipschitz regularity for local minimizers of convex variational integrals of the form \[ \mathfrak{F}( v, Ω)= \int_Ω \! F(x, Dv(x)) \, dx, \] where, for ${n > 2}$ and $N\ge 1$, $Ω$ is a bounded open set in $\mathbb{R}^n$, $u \in W^{1,1}(Ω, \mathbb{R}^N)$ and the energy density $F:Ω\times \mathbb{R}^{N \times n}\to \mathbb{R}$ satisfies the so called variable growth conditions. The main novelty of the paper is that we assume an almost critical regularity in the Orlicz Sobolev setting for the energy density as a function of the $x$ variable.
