SEMICLASSICAL PARAMETRIX FOR THE MAXWELL EQUATION AND APPLICATIONS TO THE ELECTROMAGNETIC TRANSMISSION EIGENVALUES

Georgi Vodev (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We introduce an analog of the Dirichlet-to-Neumann map for the Maxwell equation in a bounded domain. We show that it can be approximated by a pseudodifferential operator on the boundary with a matrix-valued symbol and we compute the principal symbol. As a consequence, we obtain a parabolic region free of the transmission eigenvalues associated to the Maxwell equation.

Mots clés: Maxwell equation; semiclassical parametrix; transmission eigenvalues

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Georgi Vodev. SEMICLASSICAL PARAMETRIX FOR THE MAXWELL EQUATION AND APPLICATIONS TO THE ELECTROMAGNETIC TRANSMISSION EIGENVALUES. Research in the Mathematical Sciences , 2021, 8 (3). ⟨hal-03143832⟩