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- W2040217054 abstract "We use the stochastic process called the Brownian snake to investigate solutions of the partial differential equation Δu = u2 in a domain D of class C2 of the plane. We prove that nonnegative solutions are in one-to-one correspondence with pairs (K, v) where K is a closed subset of ∂D and v is a Radon measure on ∂DK. Both Kand v are determined from the boundary behavior of the solution u. On the other hand, u can be expressed in terms of the pair (K, v) by an explicit probabilistic representation formula involving the Brownian snake. © 1997 John Wiley & Sons, Inc." @default.
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- W2040217054 date "1997-01-01" @default.
- W2040217054 modified "2023-10-05" @default.
- W2040217054 title "A probabilistic Poisson representation for positive solutions of ?u = u2 in a planar domain" @default.
- W2040217054 doi "https://doi.org/10.1002/(sici)1097-0312(199701)50:1<69::aid-cpa2>3.0.co;2-e" @default.
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