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On uniqueness in electromagnetic scattering from biperiodic structures

Armin Lechleiter, Dinh-Liem Nguyen (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Consider time-harmonic electromagnetic wave scattering from a biperiodic dielectric structure mounted on a perfectly conducting plate in three dimensions. Given that uniqueness of solution holds, existence of solution follows from a well-known Fredholm framework for the variational formulation of the problem in a suitable Sobolev space. In this paper, we derive a Rellich identity for a solution to this variational problem under suitable smoothness conditions on the material parameter. Under additional...

On variational approach to the Hamilton-Jacobi PDE

Jan H. Chabrowski, Ke Wei Zhang (1993)

Commentationes Mathematicae Universitatis Carolinae

In this paper we construct a minimizing sequence for the problem (1). In particular, we show that for any subsolution of the Hamilton-Jacobi equation ( * ) there exists a minimizing sequence weakly convergent to this subsolution. The variational problem (1) arises from the theory of computer vision equations.

On variations of the shape Hessian and sufficient conditions for the stability of critical shapes.

Marc Dambrine (2002)

RACSAM

Para el estudio de la naturaleza de formas críticas en optimización de formas se requieren algunas propiedades de continuidad sobre las derivadas de segundo orden de las formas. Dado que la fórmula de Taylor-Young involucra a diferentes topologías que no son equivalentes, dicha fórmula no permite deducir cuando una forma crítica es un mínimo local estricto de la función forma pese a que su Hessiano sea definido positivo en ese punto. El resultado principal de este trabajo ofrece una cota superior...

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