Logarithmic convexity of \(L^ 2\) norms for solutions of linear elliptic equations
type: Item
instance of: scholarly article
title: Logarithmic convexity of \(L^ 2\) norms for solutions of linear elliptic equations
zbMATH Open document ID: 0797.35030
DOI: 10.1016/0019-3577(93)90012-N
published in: Indagationes Mathematicae. New Series
publication date: 1994-10-18T00:00:00Z
review text: The author studies the problem \[ {\partial^ 2u \over \partial y^ 2} + \nabla_ x \cdot (A(x,y) \nabla_ xu) = 0 \tag{1} \] in the upper half- space \(\mathbb{R}_ +^{n+1} = \{(x,y) \in \mathbb{R}^ n \times \mathbb{R} \mid y>0\}\) and shows that there exists a function \(h\) such that \(\log \| u(x,h(y)) \|_ 2\) is convex in \(y>0\) for any solution \(u\) of (1).
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35B05
zbMATH DE Number: 549280
zbMATH Keywords: logarithmic convexity
zbMATH Keywords: linear elliptic equations
zbMATH Keywords: Hadamard three circles theorem
author: R. G. M. Brummelhuis
MaRDI profile type: Publication
cites work: Q3852455
cites work: Q3217154
cites work: Logarithmic Convexity for Supremum Norms of Harmonic Functions
cites work: A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
cites work: Q5607484
description: scientific article; zbMATH DE number 549280