On the solutions of first order partial differential equations in sets of finite perimeter with a measure as right side (Q1063779)

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.