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

2019/03/25 by А. А. Логунов, Eugenia Malinnikova, Logunov, Alexander +1 · 3 citations
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.10619

openalex publication_date 2019/03/25 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

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

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• Propagation of smallness near codimension two for gradients of harmonic functions
• Nadirashvili' Conjecture for Elliptic PDEs and its Applications
• Elliptic unique continuation below the Lipschitz threshold

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