A varifold solution to the nonlinear equation of motion of a vibrating membrane
type: Item
instance of: scholarly article
title: A varifold solution to the nonlinear equation of motion of a vibrating membrane
zbMATH Open document ID: 0631.49019
author: Daisuke Fujiwara
author: Shōichirō Takakuwa
published in: Kodai Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The authors study the ``minimal surface-wave-equation'' \[ u_{tt}- \nabla \cdot (\nabla u/\sqrt{1+| \nabla u|^ 2})=0 \] in \(\Omega \subset {\mathbb{R}}^ n\) with homogeneous boundary conditions and suitable initial conditions in the setting of geometric measure theory, especially in the framework of varifolds. They prove existence of a global varifold solution and study the relation between varifold- and BV-solutions.
Mathematics Subject Classification ID: 49Q15
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 49Q20
Mathematics Subject Classification ID: 26B30
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 4026224
zbMATH Keywords: minimal surface-wave-equation
zbMATH Keywords: geometric measure theory
zbMATH Keywords: varifolds
zbMATH Keywords: BV- solutions
reviewed by: G. Dziuk
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138037153
OpenAlex ID: W2119445031
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DOI: 10.2996/KMJ/1138037153
description: scientific article; zbMATH DE number 4026224