We study semilinear evolution equation of the type :where f and #x3BD; are given measures on o,T x #x3C9; and #x3C9; respectively, #x3C9; being a bounded open subset of IRN. We showthat (P) has a solution if and only if f and #x3BD; are not to much "concentrated" and do not charge too thin sets : the precise content of the statement involves capacities associated with suitable Sobolev's spaces. The question of removability of singularities for (P) is also completely solved.
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