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401-5753-DRL 2 Credits DR D-MATH

Carleman Estimates, Unique Continuation, and Landis Conjecture

Lecturers & Examiners: Dr. Eugenia Malinnikova
Doctoral students of I-Math (UZH) need to send an email to Jessica Bolsinger ( ) with the course number. The email should have the subject „Graduate course registration (ETH)“.
VVZ CR n/a

Last Updated: 2026-06-01 11:30:59

Abstract

Nachdiplom lecture

Content

This course will introduce Carleman estimates and their applications to unique continuation problems and the Landis conjecture. We begin with doubling properties of analytic and harmonic functions and their relation to the size of the zero set. We then develop Carleman estimates in two dimensions and discuss the Donnelly–Fefferman bounds for eigenfunctions. One of the topics will be the Landis conjecture, with special focus on the sharp growth rate for complex-valued potentials and on the two-dimensional case. Further topics include Sogge’s inequalities for spherical harmonics and their connection to the Carleman estimate of Jerison and Kenig, with applications to unique continuation for elliptic equations with lower-order terms. We will also review related results of Wolff, and of Koch and Tataru. The course concludes with frequency function methods, and recent developments on nodal sets in Lipschitz domains, domains with corners, and manifolds with singularities. Along the way, we will highlight several open problems that continue to shape research in this area.

General Information

Language
English
Levels
DR

Examination

Type
ungraded semester performance

Course Components

Type Title Time & Place Hours
lecture Carleman Estimates, Unique Continuation, and Landis Conjecture
If you plan to attend the lecture, please register by 21 September. For the registration form see
  • Mon 13:15-15:00 (HG G 43)
2 h weekly

Offered In