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Zbl 0574.35011
Carriero, M.; Leaci, A.; Pascali, E.
On the solutions of first order partial differential equations in sets of finite perimeter with a measure as right side. (Italian. English summary)
[J] Rend. Sem. Mat. Univ. Padova 73, 63-87 (1985). ISSN 0041-8994

The equation considered here is $u\sb t+\sum\sp{n}\sb{i=1}a\sb iu\sb{x\sb i}=\mu$ in E where E is a bounded set in $R\times R\sp n$ with finite perimeter, $A=(1,a\sb 1,...,a\sb n)$ is a real vector field in $L\sp{\infty}(R\times R\sp n)$ which is uniformly Lipschitz in x for a.e. t and $\mu$ is a Radon measure on the subsets of $R\times R\sp n$ satisfying some condition. The authors' goal is to prove existence, trace and localization results for the equation.
[E.Barron]

MSC 2000:: *35F05 General theory of first order linear PDE
35D05 Existence of generalized solutions of PDE

Keywords: uniqueness; continuous dependence; finite perimeter; existence; trace; localization

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