Field sensitivity to Lp variations of a scatterer

Authors

Stephen P. Shipman, Louisiana State University

Document Type

Article

Publication Date

12-1-2009

Abstract

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 (Fréchet) derivative of the scattered field measured in the H¹ (root-mean-square-gradient) norm as a function of the material coefficients measured in an L^p (p-power integral) norm, with 2 < p < ∞, 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. © 2009 Elsevier Inc. All rights reserved.

Publication Source (Journal or Book title)

Journal of Mathematical Analysis and Applications

First Page

190

Last Page

210

Recommended Citation

Shipman, S. (2009). Field sensitivity to Lp variations of a scatterer. Journal of Mathematical Analysis and Applications, 360 (1), 190-210. https://doi.org/10.1016/j.jmaa.2009.06.025