Stability of Trace Theorems on the Sphere
Stability of Trace Theorems on the Sphere
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DOI：
10.1007/s12220-017-9870-8
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
N. Bez;Chris Jeavons;Tohru Ozawa;M. Sugimoto
中科院分区：
文献类型：
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作者：
N. Bez;Chris Jeavons;Tohru Ozawa;M. Sugimoto
我们证明了球面上具有最佳常数的迹定理的稳定形式，从而获得了关于近极值的相当精确的信息。通过结合球面上的一个改进的Hardy-Littlewood-Sobolv不等式和Carlen最近证明的一个对偶稳定性结果，我们还得到了的迹定理的稳定性。最后，我们推广了Carlen对偶定理的局部形式，建立了动力学输运方程某些Strichartz估计的局部稳定性。
We prove stable versions of trace theorems on the sphere inwith optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem intofor, by combining a refined Hardy–Littlewood–Sobolev inequality on the sphere with a duality–stability result proved very recently by Carlen. Finally, we extend a local version of Carlen’s duality theorem to establish local stability of certain Strichartz estimates for the kinetic transport equation.