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A characterization of weighted Sobolev spaces and its applications

加权Sobolev空间的表征及其应用

基本信息

批准号：
16540133
负责人：
TACHIZAWA Kazuya
金额：
$ 1.98万
依托单位：
Hokkaido University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

1.We proved a weighted version of the Sobolev-Lieb-Thirring inequality. As an application we showed a weighted LP-Sobolev-Lieb-Thirring inequality which is a new result even in the non-weighted case.2.We proved that the wavelet basis is a greedy basis in weighted Triebel-Lizorkin spaces. As an application we determined the approximation spaces of the weighted Triebel-Lizorkin spaces by means of the non-linear approximation by wavelets.3.We proved a wavelet characterization of weighted Herz spaces. Tang and Yang showed a vector valued inequality in weighted Herz space although there are some mistakes in their condition on weights. We gave a correct condition on weights and proved the wavelet characterization.4.We studied the decay estimate of the solution of a non-linear elliptic partial differential equations with a potential. We characterize the class of weights in the decay estimate of the solution by the potential. We proved the global existence of a solution with small amplitude for several dispersive equations such as modified Boussinesq equations, improved Boussinesq equations and semi relativistic Hartree equations.5.We studied the existence of a singular solution and its property of a semilinear degenerate elliptic equation with p-harmonic operator in the principal term. In particular we investigated a linearized degenerate elliptic operator and proved the non-negativeness of the smallest eigenvalue and its relation to the Hardy type inequality.

1.我们证明了Sobolev-Lieb-Thirring不等式的一个加权版本。作为应用，我们给出了一个加权的LP-Sobolev-Lieb-Thirring不等式，这是在非加权情况下的一个新结果。证明了加权triiebel - lizorkin空间中的小波基是贪婪基。作为一个应用，我们利用小波的非线性逼近确定了加权triiebel - lizorkin空间的逼近空间。我们证明了加权赫兹空间的一个小波表征。Tang和Yang在加权赫兹空间中给出了一个向量值不等式，尽管他们在权重条件上存在一些错误。给出了一个正确的权值条件，并证明了小波的性质。研究了一类带势的非线性椭圆型偏微分方程解的衰减估计。我们用势来描述解的衰减估计中的权重类。证明了修正Boussinesq方程、改进Boussinesq方程和半相对论Hartree方程等色散方程小振幅解的整体存在性。研究了一类主项含p调和算子的半线性退化椭圆方程奇异解的存在性及其性质。特别地，我们研究了一个线性化的退化椭圆算子，证明了最小特征值的非负性及其与Hardy型不等式的关系。

项目成果

期刊论文数量（54）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Weighted Sobolev-Lieb-Thirring inequalities.

加权 Sobolev-Lieb-Thirring 不等式。

DOI：
发表时间：
2005
期刊：
Rev. Mat. Iberoamericana 21
影响因子：
0
作者：
Cho;Mune;H.Ishii;Kazuya Tachizawa
通讯作者：
Kazuya Tachizawa

Analytic smoothing effect for solutions to Schrodinger equations with nonlinearity of integral type

积分型非线性薛定谔方程解的解析平滑效应

DOI：
发表时间：
2005
期刊：
Osaka Journal of Mathematics 42
影响因子：
0
作者：
S.Ding;N.Murakami;H.Tomiyama;H.Takada;Y.Cho;Y.Cho;Y.Cho;Y.Cho;Y.Cho;Cho Yonggeun;Cho Yonggeun;Cho Yonggeun;Tohru Ozawa;Cho Yonggeun;Tohru Ozawa
通讯作者：
Tohru Ozawa

A generalizations of the weighted Strichartz estimates for the wave equations and an application to self-similar solutions

波动方程加权 Strichartz 估计的推广及其在自相似解中的应用