Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

On boundary regularity of solutions to Maxwell's equations with a homogeneous conservative boundary condition

Pages: 473 - 481, Volume 2, Issue 3, September 2009      doi:10.3934/dcdss.2009.2.473

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M. Eller - Department of Mathematics, Georgetown University, Washington, DC 20057, United States (email)

Abstract: The dynamic Maxwell equations with a conservative boundary condition are considered. A boundary regularity result for classical solutions is proved. This result is remarkable since the boundary condition does not satisfy the uniform Lopatinskii (Kreiss-Sakamoto) condition.

Keywords:  Maxwell's equations, boundary value problem, uniform Lopatinkii condition.
Mathematics Subject Classification:  Primary: 35L50; Secondary: 78A25.

Received: November 2008;      Revised: December 2008;      Available Online: June 2009.