A. Logunov

activity

20172021

most citedA discrete harmonic function bounded on a large portion of

Z^{2}

is constant

7 citations · 12 across the 4 of their papers we have counts for

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5 papers · 1 filter

math.AP2021

The sharp upper bound for the area of the nodal sets of Dirichlet Laplace eigenfunctions

A. Logunov, E. Malinnikova, N. Nadirashvili +1

Let $Ω$ be a bounded domain in $R^{n}$ with $C^{1}$ boundary and let $u_{λ}$ be a Dirichlet Laplace eigenfunction in $Ω$ with eigenvalue $λ$ . We show that the $(n - 1)$ -dimensio…

math.AP2021

An elliptic adaptation of ideas of Carleman and Domar from complex analysis related to Levinson's log log theorem

Alexander Logunov, Hristo Papazov

Using the three balls inequality, we adapt the elegant ideas of Carleman and Domar from complex analysis to linear elliptic PDE and generalize the classical Levinson's loglog theor…

math.AP2019

Review of Yau's conjecture on zero sets of Laplace eigenfunctions

Alexander Logunov, Eugenia Malinnikova

This is a review of old and new results and methods related to the Yau conjecture on the zero set of Laplace eigenfunctions. The review accompanies two lectures given at the confer…

math.AP2019★ 2 cited

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

Alexander Logunov, Eugenia Malinnikova

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…

math.AP2017★ 3 cited

Quantitative propagation of smallness for solutions of elliptic equations

Alexander Logunov, Eugenia Malinnikova

Let $u$ be a solution to an elliptic equation $div (A \nabla u) = 0$ with Lipschitz coefficients in $R^{n}$ . Assume $∣ u ∣$ is bounded by $1$ in the ball $B = {∣ x ∣ \leq 1}$ .…