散射体L^p变化的场灵敏度
Field sensitivity to L^p variations of a scatterer
摘要：
针对无损耗周期平板散射体对简谐标量波的衍射问题，分析了场灵敏度与平板材料系数的关系。控制方程是描述声场或电磁场的亥姆霍兹方程。主要定理建立了散射场的变分弗雷歇导数，它是在H ^1（均方根梯度）范数下测量的，作为在L^p（p次幂积分）范数下测量的材料系数的函数，其中2<p<无穷大，只要这些系数上下有正常数的界限，并且不允许共振。导数是Lipschitz连续的。我们还建立了透射能量对L^p中材料系数的变分导数。
英文摘要：
For the problem of diffraction of harmonic scalar waves by a lossless periodic slab scatterer, we analyze field sensitivity with respect to the material coefficients of the slab. The governing equation is the Helmholtz equation, which describes acoustic or electromagnetic fields. The main theorem establishes the variational Frechet derivative of the scattered field measured in the H^1 (root-mean-square-gradient) norm as a function of the material coefficients measured in an L^p (p-power integral) norm, with 2<p<infinity, as long as these coefficients are bounded above and below by positive constants and do not admit resonance. The derivative is Lipschitz continuous. We also establish the variational derivative of the transmitted energy with respect to the material coefficients in L^p.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
