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This paper is concerned with weighted energy estimates and diffusionphenomena for the initial-boundary problem of the wave equation withspace-dependent damping term in an exterior domain. In this analysis, anelliptic problem was introduced by Todorova and Yordanov. This attempt wasquite useful when the coefficient of the damping term is radially symmetric. Inthis paper, by modifying their elliptic problem, we establish weighted energyestimates and diffusion phenomena even when the coefficient of the damping termis not radially symmetric.

Remarks on an elliptic problem arising in weighted energy estimates for wave equations with space-dependent damping term in an exterior domain