Frederic Bernicot
A 2-adic approach of the human respiratory tree.
Wed, 05/05/2010 - 15:01 — SomNambulAuthors: Frederic Bernicot, Bertrand Maury, Delphine Salort
Subjects: Mathematical Physics
AbstractWe propose here a general framework to address the question of trace
operators on a dyadic tree. This work is motivated by the modeling of the human
bronchial tree which, thanks to its regularity, can be extrapolated in a
natural way to an infinite resistive tree. The space of pressure fields at
bifurcation nodes of this infinite tree can be endowed with a Sobolev space
structure, with a semi-norm which measures the instantaneous rate of dissipated
energy. We aim at describing the behaviour of finite energy pressure fields
near the end.Abstract framework for John Nirenberg inequalities and applications to Hardy spaces.
Wed, 03/03/2010 - 16:01 — SomNambulAuthors: Frederic Bernicot, Jiman Zhao
Subjects: Functional Analysis
AbstractIn this paper, we develop an abstract framework for John-Nirenberg
inequalities associated to BMO-type spaces. This work can be seen as the sequel
of [5], where the authors introduced a very general framework for atomic and
molecular Hardy spaces. Moreover, we show that our assumptions allow us to
recover some already known John-Nirenberg inequalities. We give applications to
the atomic Hardy spaces too.Stochastic perturbation of sweeping process and a convergence result for an associated numerical scheme.
Tue, 01/19/2010 - 16:01 — SomNambulAuthors: Juliette Venel, Frederic Bernicot
Subjects: Analysis of PDEs
AbstractHere we present well-posedness results for first order stochastic
differential inclusions, more precisely for sweeping process with a stochastic
perturbation. These results are provided in combining both deterministic
sweeping process theory and methods concerning the reflection of a Brownian
motion. In addition, we prove convergence results for a Euler scheme,
discretizing theses stochastic differential inclusions.
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