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arXiv · 1903.10619

Lecture notes on quantitative unique continuation for solutions of second order elliptic equations

Alexander Logunov·Eugenia Malinnikova
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Abstract

In these lectures we present some useful techniques to study quantitative properties of solutions of elliptic PDEs. Our aim is to outline a proof of a recent result on propagation of smallness. The ideas are also useful in the study of the zero sets of eigenfunctions of Laplace-Beltrami operator and we discuss the connection. Some basic facts about second order elliptic PDEs in divergent form are collected in the Appendix at the end of the notes.

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Alexander Logunov, Eugenia Malinnikova. 2019-03-25. Lecture notes on quantitative unique continuation for solutions of second order elliptic equations. https://arxiv.org/abs/1903.10619

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