论文标题
基于最大L_P-L_Q空间的抛物线方程的较高规律性
Higher regularity for parabolic equations based on maximal L_p-L_q spaces
论文作者
论文摘要
在本文中，我们证明了具有一般边界条件的2m-ther阶抛物线方程的较高规律性。这是一种具有可怜性的最大L_P-L_Q规则性，即主要定理是使用BESOV和TRIEBEL--LIZORKIN空间之间的解决方案空间和数据空间之间的同构。关键是初始数据的兼容条件。如果满足兼容性条件的数据平滑，我们将能够获得独特的平滑解决方案。
In this paper we prove higher regularity for 2m-th order parabolic equations with general boundary conditions. This is a kind of maximal L_p-L_q regularity with differentiability, i.e. the main theorem is isomorphism between the solution space and the data space using Besov and Triebel--Lizorkin spaces. The key is compatibility conditions for the initial data. We are able to get a unique smooth solution if the data satisfying compatibility conditions are smooth.
