Approximation of minimal surfaces with free boundaries
type: Item
instance of: scholarly article
title: Approximation of minimal surfaces with free boundaries
zbMATH Open document ID: 1448.53010
DOI: 10.4171/IFB/412
author: Ulrich Dierkes
author: Tristan Jenschke
author: Paola Pozzi
published in: Interfaces and Free Boundaries
publication date: 2019-02-28T00:00:00Z
review text: The authors develop a penalty method to approximate solutions of the free boundary problem for minimal surfaces. For this goal they study the problem of finding minimizers of a certain functional which is defined as the sum of the Dirichlet integral as well as an appropriate penalty term weighted by a parameter \(\lambda\). They show -- among other things -- the existence of a solution when \(\lambda\) is large enough and the convergence to a solution of the free boundary problem in the case when the parameter \(\lambda\) tends to infinity. Regularity at the boundary of these solutions is obtained.
reviewed by: Themistocles M. Rassias
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 49Q05
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 7031093
zbMATH Keywords: minimal surfaces
zbMATH Keywords: stationary surfaces
zbMATH Keywords: Dirichlet integral
zbMATH Keywords: harmonic solution
zbMATH Keywords: harmonic extension
zbMATH Keywords: free boundary problem
zbMATH Keywords: finite element approximation
zbMATH Keywords: convergence
MaRDI profile type: Publication
cites work: Numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces
cites work: Minimal Surfaces
cites work: Global Analysis of Minimal Surfaces
cites work: Regularity of Minimal Surfaces
cites work: The discrete Plateau Problem: Algorithm and numerics
cites work: The discrete plateau problem: Convergence results
cites work: Q3408825
cites work: Q5187597
cites work: Approximation of minimal surfaces with free boundaries: convergence results
cites work: Q5628582
cites work: Multiple integrals in the calculus of variations
cites work: 𝐿²-estimate for the discrete Plateau Problem
cites work: Q5169416
cites work: Q4707153
full work available at URL: https://doi.org/10.4171/ifb/412
OpenAlex ID: W2905392163
Wikidata QID: Q128759325
description: scientific article; zbMATH DE number 7031093