论文标题
与线性PDE相关的非局部运算符的功能和变异方面
Functional and variational aspects of nonlocal operators associated with linear PDEs
论文作者
论文摘要
我们为与一阶线性运算符相关的非本地运算符引入了一般差异商表示。我们在功能，度量和分布的各个空间中建立了新的本地至非本地估计和强大的本地化原则，这些原理完全概括为梯度已知的那些。在适当的假设下，我们还建立了拟议的局部非局部环境中准室性的不变性。进一步讨论了$ \ Mathcal $级级别措施的良好属性的应用。
We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of functions, measures and distributions, which fully generalize those known for gradients. Under suitable assumptions, we also establish the invariance of quasiconvexity within the proposed local-nonlocal setting. Applications to the fine properties of $\mathcal A$-gradient measures are further discussed.
