On Tensorial Estimates, Sharp Trace Theorems, and Parallel Scalar Reductions

Details On Tensorial Estimates, Sharp Trace Theorems, and Parallel Scalar Reductions On Tensorial Estimates, Sharp Trace Theorems, and Parallel Scalar Reductions

2012-02-06

arxiv.org/abs/1202.1295v1

Mathematics

Analysis of PDEs

54 pages

Scientific paper

In this paper, we consider various bilinear product and integrated product estimates on a one-parameter foliation of surfaces with evolving geometries. Moreover, we wish to do this with only very weak control on how the geometries evolve. Several of these estimates were established in previous work by S. Klainerman and I. Rodnianski, in very special settings. A primary objective of this paper is to significantly simplify the proofs of the existing results. Another goal is to generalize these existing estimates to more abstract settings.

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