论文标题
$（p，q）$增长的一类障碍问题的有限解决方案的较高的可不同性能
Higher differentiability for bounded solutions to a class of obstacle problems with $(p,q)$-growth
论文作者
论文摘要
我们建立了有限的最小化器对一类障碍问题的较高的分数可不同性，形式的非标准生长条件{gatch*} \ min \ min \ biggl \ {\ displayStyle \ displayStyle \int_Ωf（x，x，x，d t x，d t x，d t x，dw）dx \：\ w \ in \ in \ mathcal in \ mathcal {grogen {grogen {kig} big {其中$ω$是$ \ mathbb {r}^n $，$ n \ geq 2 $的有界开放集\ geqψ\ \ text {a.e。 in} \ω\} $是一类可允许的功能。如果障碍物$ψ$是本地界限的，我们证明解决方案的梯度继承了某些分数可不同性属性，假设障碍物的梯度和映射$ x \ mapstod_ξf（x，ξ）$属于一些合适的besov空间。主要新颖的是，这种假设与尺寸$ n $无关。
We establish the higher fractional differentiability of bounded minimizers to a class of obstacle problems with non-standard growth conditions of the form \begin{gather*} \min \biggl\{ \displaystyle\int_Ω F(x,Dw)dx \ : \ w \in \mathcal{K}_ψ(Ω) \biggr\}, \end{gather*} where $Ω$ is a bounded open set of $\mathbb{R}^n$, $n \geq 2$, the function $ψ\in W^{1,p}(Ω)$ is a fixed function called \textit{obstacle} and $\mathcal{K}_ψ(Ω) := \{ w \in W^{1,p}(Ω) : w \geq ψ\ \text{a.e. in} \ Ω\}$ is the class of admissible functions. If the obstacle $ψ$ is locally bounded, we prove that the gradient of solution inherits some fractional differentiability property, assuming that both the gradient of the obstacle and the mapping $x \mapsto D_ξF(x,ξ)$ belong to some suitable Besov space. The main novelty is that such assumptions are not related to the dimension $n$.
