Student Harmonic Analysis and PDE Seminar (HADES): $L^p$ estimates on eigenfunctions for low regularity metrics

Seminar | February 20 | 3:30-5 p.m. | 740 Evans Hall

 Albert Ai, UC Berkeley

 Department of Mathematics

We will consider $L^p$ estimates on eigenfunctions for elliptic operators on manifolds with low regularity (Lipschitz) metrics. To address the low regularity, we use a wave packet decomposition to reduce to estimates at a scale on which the Lipschitz coefficients can be approximated by $C^2$ coefficients. To obtain sharp results however, we also need to consider the possible energy overlap at an intermediate scale. This talk is based on a paper of Koch-Smith-Tataru.