S. M. Berge

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20192022

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math.AP2021

Kuttler-Sigillito's Inequalities and Rellich-Christianson Identity

Stine Marie Berge

This article has two main objectives. The first one is to show Kuttler-Sigillito's type inequalities involving the mixed Neumann-Dirichlet, mixed Steklov-Dirichlet, and mixed Robin…

math.AP2020

On the three ball theorem for solutions of the Helmholtz equation

Stine Marie Berge, Eugenia Malinnikova

Let $u_{k}$ be a solution of the Helmholtz equation with the wave number $k$ , $Δ u_{k} + k^{2} u_{k} = 0$ , on a small ball in either $R^{n}$ , $S^{n}$ , or $H^{n}$ . For a fix…

math.AP2019

Convexity Properties of Harmonic Functions on Parameterized Families of Hypersurfaces

Stine Marie Berge

It is known that the $L^{2}$ -norms of a harmonic function over spheres satisfies some convexity inequality strongly linked to the Almgren's frequency function. We examine the $L^{2…