A probabilistic Poisson representation f
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Jean-François Le Gall
📂
Article
📅
1997
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John Wiley and Sons
🌐
English
⚖ 255 KB
We use the stochastic process called the Brownian snake to investigate solutions of the partial differential equation ∆u = u 2 in a domain D of class C 2 of the plane. We prove that nonnegative solutions are in one-to-one correspondence with pairs (K, ν) where K is a closed subset of ∂D and ν is a R