The Dirichlet problem on a strip for the \(\alpha\)-translating soliton equation
type: Item
instance of: scholarly article
title: The Dirichlet problem on a strip for the \(\alpha\)-translating soliton equation
zbMATH Open document ID: 1455.35216
author: Rafael López
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2018-12-17T00:00:00Z
review text: The paper studies the existence of classical solutions \(u\in C^2(\Omega)\cap C^0(\partial\Omega)\) to the Dirichlet problem, \[ \text{div}\left(\frac{Du}{\sqrt{1+|Du|^2}}\right)=\left(\frac{1}{\sqrt{1+|Du|^2}}\right)^\alpha \text{ in } \Omega, \] \[u=\phi \text{ on }\partial\Omega.\] where \(\Omega\subset \mathbb{R}^2\) is a smooth domain, \(\alpha\) is a positive constant, and \(\phi\in C^0(\partial\Omega)\). In particular, the author proves the existence of solutions when \(\Omega\) is a strip of \(\mathbb{R}^2\), using the Perron method and a family of grin reapers as barriers.
reviewed by: Solomon Manukure
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 53C45
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 35A01
zbMATH DE Number: 6994059
zbMATH Keywords: Dirichlet problem, Perron method, translating soliton, grim reapers
MaRDI profile type: Publication
full work available at URL: j.crma.2018.10.005
OpenAlex ID: W2899198387
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DOI: 10.1016/J.CRMA.2018.10.005
description: scientific article; zbMATH DE number 6994059