Eine Bemerkung zur Hebbarkeit gewisser isolierter Singularitäten bei nichtlinearen elliptischen Systemen
type: Item
instance of: scholarly article
title: Eine Bemerkung zur Hebbarkeit gewisser isolierter Singularitäten bei nichtlinearen elliptischen Systemen
zbMATH Open document ID: 0549.35042
DOI: 10.1007/BF01237862
published in: Archiv der Mathematik
publication date: 1985-01-01T00:00:00Z
review text: We consider weak solutions \(u:\Omega\to {\mathbb{R}}^ N\) of elliptic systems \(-D_{\alpha}(a_{\alpha\beta } D_{\beta} u)=f(\cdot,u,Du)\) where f is of quadratic growth in Du. Defining the geometric dimension of an isolated singularity \(x_ 0\) of u we show that \(x_ 0\) is removable for small dimensions. So the standard smallness condition in regularity theory relating the modulus of ellipticity, the oscillation of u and the constant a in \(| f(\cdot,u,Du)|\leq a\cdot| Du|^ 2+b\) can be replaced by the condition that dim x\({}_ 0\) is sufficiently small.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35A20
zbMATH DE Number: 3875821
zbMATH Keywords: removable singularity
zbMATH Keywords: weak solutions
zbMATH Keywords: elliptic systems
zbMATH Keywords: geometric dimension
zbMATH Keywords: isolated singularity
zbMATH Keywords: smallness condition
author: M. Fuchs
MaRDI profile type: Publication
cites work: Harmonic mappings and minimal submanifolds
cites work: Q3662317
cites work: Some regularity results for quasilinear elliptic systems of second order
cites work: Q4123700
cites work: Ein optimaler Regularitätssatz für schwache Lösungen gewisser elliptischer Systeme
full work available at URL: https://doi.org/10.1007/bf01237862
OpenAlex ID: W2045479144
description: scientific article; zbMATH DE number 3875821