On the solutions of first order partial differential equations in sets of finite perimeter with a measure as right side
type: Item
instance of: scholarly article
title: On the solutions of first order partial differential equations in sets of finite perimeter with a measure as right side
zbMATH Open document ID: 0574.35011
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/107990
review text: The equation considered here is \(u_ t+\sum^{n}_{i=1}a_ iu_{x_ i}=\mu\) in E where E is a bounded set in \(R\times R^ n\) with finite perimeter, \(A=(1,a_ 1,...,a_ n)\) is a real vector field in \(L^{\infty}(R\times R^ n)\) which is uniformly Lipschitz in x for a.e. t and \(\mu\) is a Radon measure on the subsets of \(R\times R^ n\) satisfying some condition. The authors' goal is to prove existence, trace and localization results for the equation.
Mathematics Subject Classification ID: 35F05
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 3916812
zbMATH Keywords: uniqueness
zbMATH Keywords: continuous dependence
zbMATH Keywords: finite perimeter
zbMATH Keywords: existence
zbMATH Keywords: trace
zbMATH Keywords: localization
author: M. Carriero
author: A. Leaci
author: Eduardo Pascali
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3916812