论文标题
更高的可不同性导致BESOV空间的规模到一类双相障碍问题
Higher differentiability results in the scale of Besov spaces to a class of double-phase obstacle problems
论文作者
论文摘要
我们研究了解决方案梯度梯度的较高分数可分离性能，即形式的变化障碍物问题\ begin {chater*} \ min \ biggl \ {\int_Ωf（x，x，x，x，w，d，dw）d x \：\ w \ in \ nathcal {k}_ψ（k}）表格\ begin {qore*} f（x，w，z）= b（x，w）（| z | | |^p+a（x）| z |^q），\ end {equation*}，其中$ω$是$ \ \ mthbb {r}^n $ in w^n $ in w^in w^^in w^^^^^^{1，p^{1，p^{ \ textit {障碍}和$ \ Mathcal {k}_ψ（ω）= \ {w \ in W^{1，p}（p}（ω）：w \ geqψ\ \ text {a.e。 in} \ω\} $是一类可允许的功能。假设障碍物的梯度属于合适的BESOV空间，我们能够证明该解决方案的梯度保留了一些分数可不同性属性。
We study the higher fractional differentiability properties of the gradient of the solutions to variational obstacle problems of the form \begin{gather*} \min \biggl\{ \int_Ω F(x,w,Dw) d x \ : \ w \in \mathcal{K}_ψ(Ω) \biggr\}, \end{gather*} with $F$ double phase functional of the form \begin{equation*} F(x,w,z)=b(x,w)(|z|^p+a(x)|z|^q), \end{equation*} where $Ω$ is a bounded open subset of $\mathbb{R}^n$, $ψ\in W^{1,p}(Ω)$ 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. Assuming that the gradient of the obstacle belongs to a suitable Besov space, we are able to prove that the gradient of the solution preserves some fractional differentiability property.
