On the maximal Lp-regularity of parabolic mixed-order systems
On the maximal Lp-regularity of parabolic mixed-order systems
复制标题
抛物型混阶系统的最大Lp正则性
DOI：
--
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
J. Seiler
中科院分区：
文献类型：
--
作者：
R. Denk;J. Seiler
研究了时空柱上一类拟微分混合阶系统的极大Lp-正则性 imes mathbb{R}}$$或$${X imes mathbb{R}}$$，其中X是闭合光滑流形。为此，我们构造了一个演算的沃尔泰拉伪微分算子和特征的抛物性系统的某些相关符号的可逆性。本文证明了一个抛物系统在合适的Bessel势或Besov型Lp-Sobolev空间之间诱导同构。如果时空柱的横截面是紧的，抛物系统的逆又属于微积分。作为应用，我们讨论了含时的Douglis-Nirenberg系统和一个线性系统在研究具有Gibbs-Thomson修正的Stefan问题时出现的问题。
We study maximal Lp-regularity for a class of pseudodifferential mixed-order systems on a space–time cylinder $${mathbb{R}^n imes mathbb{R}}$$ or $${X imes mathbb{R}}$$ , where X is a closed smooth manifold. To this end, we construct a calculus of Volterra pseudodifferential operators and characterize the parabolicity of a system by the invertibility of certain associated symbols. A parabolic system is shown to induce isomorphisms between suitable Lp-Sobolev spaces of Bessel potential or Besov type. If the cross section of the space–time cylinder is compact, the inverse of a parabolic system belongs to the calculus again. As applications, we discuss time-dependent Douglis–Nirenberg systems and a linear system arising in the study of the Stefan problem with Gibbs–Thomson correction.