Solution surfaces for semilinear elliptic equations on rotated domains
type: Item
instance of: scholarly article
title: Solution surfaces for semilinear elliptic equations on rotated domains
zbMATH Open document ID: 0953.35045
author: Seth Armstrong
author: Renate Schaaf
published in: Advances in Differential Equations
publication date: 2000-08-21T00:00:00Z
review text: The authors consider the problem \(\Delta u+\lambda f(u)=0\) in \(\Omega_\varepsilon\), \(u=0\) on \(\partial\Omega_\varepsilon\), where \(\Omega_\varepsilon\) is a torus-like domain in \(\mathbb{R}^{n+1}\) obtained from \(\Omega\) by a translation \({1\over\varepsilon}\) and a rotation about an axis. For \(\Omega\in \mathbb{R}^2\) (with symmetry and convexity assumptions) or \(\Omega\) a ball in \(\mathbb{R}^2\) they prove the existence of a solution surface in \((\alpha,\varepsilon)\), where \(\alpha=\max u\) and \(\varepsilon\) is sufficiently small, together with some additional interesting properties.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47J05
zbMATH DE Number: 1493593
zbMATH Keywords: torus-like domain
zbMATH Keywords: symmetry
zbMATH Keywords: convexity
zbMATH Keywords: existence
reviewed by: René Sperb
MaRDI profile type: Publication
Recommended article: Q4703034
Recommended article: A Note on the Complete Rotational Invariance of Biradial Solutions to Semilinear Elliptic Equations
Recommended article: On the Cheeger problem for rotationally invariant domains
Recommended article: Solutions of systems of elliptic differential equations on circular domains
Recommended article: Solutions on a torus for a semilinear equation
Recommended article: Semilinear elliptic problems on domains with corners
Recommended article: Infinitely Many Rotationally Symmetric Solutions to a Class of Semilinear Laplace–Beltrami Equations on Spheres
Recommended article: Q4697954
Recommended article: Solutions of a Nonlinear Dirichlet Problem for Nearly Circular Domains
Recommended article: Q3488520
description: scientific article; zbMATH DE number 1493593