On the trace of the wave group and regularity of potentials

2021/04/02 by Hart F. Smith, Smith, Hart F. · 1 citation
Mathematics · #46E35 #58J45 #58J50 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:46E35 #msc:58J45 #msc:58J50

paper · pdf · doi:10.48550/arxiv.2104.00833

31 pages

arxiv created 2021/04/02 · arxiv updated 2021/04/05

Abstract

For the wave equation ∂_t²-Δ+V on ℝ^d with compactly supported, real valued potential V, we establish a sharp relation between Sobolev regularity of V and the existence of finite order expansions as t→ 0 for the relative trace of the wave group.

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