An Elliptic Regularity Coefficient Estimate for a Problem Arising from a Frequency Domain Treatment of Waves

Abstract

Abstract. We consider a sequence of noncoercive elliptic problems, which are the wave equation in the frequency domain, in a rectangular or cubic domain with an absorbing boundary condition. The elliptic regularity coefficient depends on the frequency, and it has a singularity for both zero and infinite frequency. In this paper we derive an elliptic regularity estimate as the frequency tends to zero and infinity.