A symmetric positive system with nonuniformly characteristic boundary.
type: Item
instance of: scholarly article
title: A symmetric positive system with nonuniformly characteristic boundary.
zbMATH Open document ID: 1131.35324
author: Paolo Secchi
published in: Differential and Integral Equations
publication date: 2000-05-29T00:00:00Z
review text: The boundary value problem \(Mu =g\) on \(\partial \Omega \) for the linear system of \(k\) equations \(Lu = f\) on a bounded Lipschitz (or smooth) domain \(\Omega \subset \mathbb R^n\) is considered, where \(L = \sum ^n_{j=1} A_j\partial /\partial x_j + B\) with \(A_j, B\), and \(M\) being \((k\times k)\)-matrix valued functions of \(x\). In case of noncharacteristic boundary conditions, \(L^2\)- or \(H^1\)-solutions are proved to exist. For \(M(\cdot )\) not of a constant rank and alternating definiteness between positive and negative, existence of regular solutions is investigated, too.
reviewed by: Tomáş Roubíçek
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 35F15
Mathematics Subject Classification ID: 35L50
zbMATH DE Number: 1453651
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1453651