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On Uniqueness of a Solution of Lu=u^a with Given Trace
superdiffusion moderate solutions trace of a solution explosion points
2009/5/4
A boundary trace (G, m) of a solution of Delta u = u^a in a bounded smooth domain in R^d was first constructed by Le Gall who described all possible traces for a = 2, d= 2 in which case a solution is ...
Uniqueness of the mixing measure for a random walk in a random environment on the positive integers
random walk in a random environment mixingmeasure
2009/4/29
Consider a random walk in an irreducible random environment on the positive integers. We prove that the annealed law of the random walk determines uniquely the law of the random environment. An applic...
Uniqueness of multi-dimensional infinite volume self-organized critical forest-fire models
forest-fires self-organized criticality forest-fire model unique adapted
2009/4/23
In a forest-fire model, each site of the square lattice is either vacant or occupied by a tree. Vacant sites get occupied according to independent rate 1 Poisson processes. Independently at each site ...
Pathwise uniqueness for reflecting Brownian motion in certain planar Lipschitz domains
reecting Brownian motion
2009/4/22
We give a simple proof that in a Lipschitz domain in two dimensions with Lipschitz constant one, there is pathwise uniqueness for the Skorokhod equation governing reflecting Brownian motion.