Estimates of scattered electromagnetic fields. (19th August 2013)

• Record Type: Journal Article
• Authors: Wellander, N.; Kristensson, G.; Barbatis, Gerassimos; Stratis, Ioannis
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 2(2014:Jan. 30)
• Page Start: 167
• Page End: 172
• Publication Date: 2013-08-19
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2831
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2831-abs-0001"> <title>Abstract</title> <p id="mma2831-para-0001">We present some general estimates of the scattered electromagnetic fields for a general bounded scattering domain Ω in the anisotropic materials setting. In particular, it is shown that the <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4t700gjf" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="block" altimg="urn:x-wiley:01704214:media:mma2831:mma2831-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo class="MathClass-rel">∥</mml:mo><mml:mo class="MathClass-bin">⋅</mml:mo><mml:msub><mml:mrow><mml:mo class="MathClass-rel">∥</mml:mo></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mrow><mml:mo class="MathClass-open">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>Ω</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">s</mml:mi></mml:mrow></mml:msub><mml:mo class="MathClass-punc">;</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">C</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo class="MathClass-close">)</mml:mo></mml:mrow></mml:mrow></mml:msub></mml:math></alternatives> ‐ norm and sup norm of the scattered field in an arbitrary finite exterior domain Ω<sub>s</sub> is bounded by the <italic>H</italic>(curl, Ω) norm of the incident field. Moreover, several estimates of the traces of the scattered field on the boundary are presented. These estimates have bearing on estimations on cloaking. Copyright © 2013 John Wiley & Sons, Ltd.</p> </abstract>