Resolves Sogge’s local smoothing conjecture for the Euclidean wave equation in three spatial dimensions. The estimate holds throughout the full strict range \(2\lt p\lt \infty\), with Sobolev regularity above \(\max\{0,1-3/p\}\). In particular, the critical L3 estimate holds with every positive Sobolev loss.
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In Critical local smoothing for the three-dimensional wave equation, 24 September 2026
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For every \eps>0 there exists C_\eps<\infty such that
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Theorem 1.1 (Critical local smoothing)
In Critical local smoothing for the three-dimensional wave equation, 24 September 2026