OpenAI research collection · 1 manuscript · Source checked 2026-10-19
Resolves Sogge's local smoothing conjecture for the Euclidean wave equation in three spatial dimensions. The estimate holds throughout the full strict range 2< p< ∞, with Sobolev regularity above \max\{0,1-3/p\}. In particular, the critical L^(3) estimate holds with every positive Sobolev loss.
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We prove the critical L^(3) local smoothing estimate for the wave equation in three spatial dimensions, with every positive Sobolev loss. This resolves Sogge's Euclidean local smoothing conjecture in dimension three.
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