A note on removable singularities for minima of certain vector-valued obstacle problems
type: Item
instance of: scholarly article
title: A note on removable singularities for minima of certain vector-valued obstacle problems
zbMATH Open document ID: 0608.49006
DOI: 10.1007/BF01190359
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: We analyze the regularity properties of vector-valued functions \(u: {\mathbb{R}}^ n\supset D\to {\mathbb{R}}^ N\) minimizing a quadratic variational integral \[ F(u):=\sum ^{N}_{i=1}\sum ^{n}_{\alpha,\beta =1}\int _{D}a_{\alpha \beta}(\cdot,u)D_{\alpha}u^ iD_{\beta}u^ idx \] under an additional side-condition of the form Im(u)\(\subset \bar M\) for a smooth region M in \({\mathbb{R}}^ N\). We try to exhibit reasonable geometric conditions on the set M excluding singular points. For example we show that the singular set is empty if M is a star-like domain of sufficiently small diameter. A counter-example demonstrates the sharpness of our result.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
zbMATH DE Number: 3983973
zbMATH Keywords: regularity
zbMATH Keywords: quadratic variational integral
zbMATH Keywords: singular set
zbMATH Keywords: vector-valued obstacle problems
author: M. Fuchs
MaRDI profile type: Publication
cites work: Variational inequalities and harmonic mappings.
cites work: Variational problems with non-convex obstacles and an integral constraint for vector-valued functions
cites work: Optimal regularity theorems for variational problems with obstacles
cites work: Variational inequalities for vector-valued functions with non-convex obstacles
cites work: Some remarks on the boundary regularity for minima of variational problems with obstacles
cites work: Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
cites work: Q4123700
cites work: Q4195495
cites work: Q3663717
cites work: Variationsprobleme vom Dirichlet-Typ mit einer Ungleichung als Nebenbedingung
cites work: On minima of variational problems with some nonconvex constraints
full work available at URL: https://doi.org/10.1007/bf01190359
OpenAlex ID: W2011527853
description: scientific article; zbMATH DE number 3983973