Dispersive estimates for the wave equation on Riemannian manifolds of bounded curvature
| Autor: | Hart F. Smith, Yuanlong Chen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Riemann curvature tensor
Ocean Engineering Lebesgue integration 01 natural sciences symbols.namesake Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics dispersive estimates Tensor 0101 mathematics Mathematics 58J45 (Primary) 35L15 (Secondary) 010102 general mathematics Mathematical analysis Wave equation 58J45 Sobolev space Range (mathematics) 35L15 Bounded function symbols wave equation 010307 mathematical physics Mathematics::Differential Geometry Metric tensor (general relativity) Analysis of PDEs (math.AP) |
| Zdroj: | Pure Appl. Anal. 1, no. 1 (2019), 101-148 |
| Popis: | We establish space-time dispersive estimates for solutions to the wave equation on compact Riemannian manifolds with bounded sectional curvature, with the same exponents as for $C^\infty$ metrics. The estimates are for bounded time intervals, so by finite propagation velocity the results apply also on non-compact manifolds under appropriate uniform conditions. We assume a priori that in local coordinates the metric tensor components satisfy ${\rm g}_{ij}\in W^{1,p}$ for some $p>d$, which ensures that the curvature tensor is well defined in the weak sense, but this can be relaxed to any assumption that suffices for the local harmonic coordinate calculations in the paper. |
| Databáze: | OpenAIRE |
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