论文标题
临界电磁场中的衰减和Strichartz估计值
Decay and Strichartz estimates in critical electromagnetic fields
论文作者
论文摘要
我们研究了aharonov-bohm磁场中分散方程的$ l^1 \ to l^\ infty $ decay估计，并进一步证明了具有关键电磁电位的klein-gordon方程的strichartz估计值。新颖的成分是在Aharonov-Bohm磁场中为Schrödingeroberator的光谱度量和热传播器的Schwartz内核的构建。特别是，我们明确构建具有Aharonov-bohm电位的Schrödinger操作员的光谱度量和解决方案的表示，并表明关键电磁场中的热核可以满足高斯界限。在将来的论文中，该频谱度量的结果将用于（i）研究均匀的分解估计，（ii）在同一环境中证明波传播的$ l^p $ regularity属性。
We study the $L^1\to L^\infty$-decay estimates for dispersive equations in the Aharonov-Bohm magnetic fields, and further prove Strichartz estimates for the Klein-Gordon equation with critical electromagnetic potentials. The novel ingredients are the construction of Schwartz kernels of the spectral measure and heat propagator for the Schrödinger operator in Aharonov-Bohm magnetic fields. In particular, we explicitly construct the representation of the spectral measure and resolvent of the Schrödinger operator with Aharonov-Bohm potentials, and show that the heat kernel in critical electromagnetic fields satisfies Gaussian boundedness. In future papers, this result on the spectral measure will be used to (i) study the uniform resolvent estimates, and (ii) prove the $L^p$-regularity property of wave propagation in the same setting.
