[PDF.35eg] Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation (Memoirs of the American Mathematical Society Series No. 798)

Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation (Memoirs of the American Mathematical Society Series No. 798)

[PDF.tf06] Classification and Probabilistic Representation of the Positive Solutions of a Semilinear Elliptic Equation (Memoirs of the American Mathematical Society Series No. 798)

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 | #19187243 in Books |  American Mathematical Society (AMS) |  2004-03-01 | Original language:English |  10.04 x.20 x6.97l,1.10 | File type: PDF | 121 pages

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We are concerned with the nonnegative solutions of $\Delta u = u^2$ in a bounded and smooth domain in $\mathbb{R}^d$. We prove that they are uniquely determined by their fine trace on the boundary as defined in [DK98a], thus answering a major open question of [Dy02]. In this title, a probabilistic formula for a solution in terms of its fine trace and of the Brownian snake is also provided. A major role is played by the solutions which are dominated by a harmonic function...

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