论文标题
Schauder估计退化LévyOrnstein-Ulhenbeck运营商
Schauder estimates for degenerate Lévy Ornstein-Ulhenbeck operators
论文作者
论文摘要
我们使用一些适用于椭圆形和抛物线的抛物线设置，建立了可能是否定的lévyornstein-uhlenbeck运算符驱动的全球舒特尔估计值（IPDE）。我们认为的运算符类是由线性漂移加上Lévy操作员组成的，该操作员在适当的意义上与可能截断的稳定操作员相当。例如，它包括相对论，纠正，分层或Lamperti稳定的操作员。我们的方法既不假设Lévy操作员的对称性也不是对操作员线性部分扩张的不变性。得益于我们的估计，我们还证明了在合适的功能空间中所考虑的IPDE的适当性。在最后一部分中，我们将其中一些结果扩展到涉及非线性，时空依赖性漂移的更普通运算符。
We establish global Schauder estimates for integro-partial differential equations (IPDE) driven by a possibly degenerate Lévy Ornstein-Uhlenbeck operator, both in the elliptic and parabolic setting, using some suitable anisotropic Hölder spaces. The class of operators we consider is composed by a linear drift plus a Lévy operator that is comparable, in a suitable sense, with a possibly truncated stable operator. It includes for example, the relativistic, the tempered, the layered or the Lamperti stable operators. Our method does not assume neither the symmetry of the Lévy operator nor the invariance for dilations of the linear part of the operator. Thanks to our estimates, we prove in addition the well-posedness of the considered IPDE in suitable functional spaces. In the final section, we extend some of these results to more general operators involving non-linear, space-time dependent drifts.
