On parabolic equations in one space dimension
On parabolic equations in one space dimension
复制标题
一维抛物线方程
DOI：
10.1080/03605302.2015.1126734
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发表时间：
2015
影响因子：
1.9
通讯作者：
N. Krylov
中科院分区：
文献类型：
--
作者：
N. Krylov
摘要 对于一维空间中没有低阶项的非齐次二阶均匀抛物线方程，提出了关于柯西问题 Sobolev 类可解性的几个负面结果。主系数被假设为 (t, x) 的有界可测函数，其边界远离 0。我们还讨论了此类方程的基本解的某种类型的上限和下限估计。
ABSTRACT Several negative results are presented concerning the solvability in Sobolev classes of the Cauchy problem for the inhomogeneous second-order uniformly parabolic equations without lower order terms in one space dimension. The main coefficient is assumed to be a bounded measurable function of (t, x) bounded away from 0. We also discuss upper and lower estimates of certain kind on the fundamental solutions of such equations.