Wave decay for star-shaped obstacles in mathbb{R}³: papers of Morawetz and Ralston revisited
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🧮 math.SP
math-phmath.APmath.MP
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bounddecaylowermorawetzobstaclesralstonstar-shapeddirichlet
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The purpose of this expository note is to revisit Morawetz's method for obtaining a lower bound on the rate of exponential decay of waves for the Dirichlet problem outside star-shaped obstacles, and to discuss the uniqueness of the sphere as the extremizer of the sharp lower bound proved by Ralston.
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