Instanteneous smoothing estimates for the Hermite semigroup in uniformly local spaces and related nonlinear equations
Instanteneous smoothing estimates for the Hermite semigroup in uniformly local spaces and related nonlinear equations
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均匀局部空间中Hermite半群的瞬时平滑估计及相关非线性方程
DOI：
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发表时间：
2004
影响因子：
0.3
通讯作者：
P. Souplet
中科院分区：
文献类型：
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作者：
J. Matos;P. Souplet
我们考虑Hermite半群，由运营商？-？y.？在RN。
在一致空间中建立了Hermite半群的瞬时光滑估计
Kato [1]引入的局部Lebesgue空间。
从纳尔逊[3]和Gross [2]的经典著作中可以知道，这种smooting性质在通常的加权Lebesgue空间中是不成立的。这个线性结果使我们能够证明一些相关的瞬时平滑估计
非线性抛物问题
We consider the Hermite semigroup, generated by the operator ?-?y.? in RN.
We establish instantaneous smoothing estimates for the Hermite semigroup in the uniformly
local Lebesgue spaces introduced by Kato [1].
It was known from the classical works of Nelson [3] and Gross [2] that such smooting properties fail in usual weighted Lebesgue spaces. This linear result enables us to prove instantaneous smoothing estimates for some related
nonlinear parabolic problems.