Wave decay for star-shaped obstacles in $\mathbb{R}^3$: papers of Morawetz and Ralston revisited

Peter Hintz; Maciej Zworski

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arXiv · 1703.01389

Wave decay for star-shaped obstacles in $\mathbb{R}^3$: papers of Morawetz and Ralston revisited

Peter Hintz·Maciej Zworski

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Abstract

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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BibTeX RIS

Peter Hintz, Maciej Zworski. 2017-03-04. Wave decay for star-shaped obstacles in $\mathbb{R}^3$: papers of Morawetz and Ralston revisited. https://arxiv.org/abs/1703.01389

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