About semilineat low dimension Bessel PDEs
soumis
Type de publication :
Article (revues avec comité de lecture)
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arXiv :
Mots clés :
SDEs with distributional drift; Bessel processes; Kolmogorov equation; mild and weak solutions; self-adjoint operators; Friedrichs extension.
Résumé :
We prove existence and uniqueness of
solutions of a semilinear PDE driven by a Bessel type generator
$L^\delta$ with low dimension $0 < \delta < 1$.
$L^\delta$ is a local operator, whose drift is the
derivative of $x \mapsto \log (\vert x\vert)$:
in particular it is a Schwartz distribution, which
is not the derivative of a continuous function.
The solutions
are intended in a duality ("weak") sense
with respect to state space
$L^2(\R_+, d\mu),$ $\mu$ being
an invariant measure for the Bessel semigroup.
BibTeX :
@article{Oha-Rus-Tei-2200,
author={Alberto Ohashi and Francesco Russo and Alan Teixeira },
title={About semilineat low dimension Bessel PDEs },
year={soumis },
month={3},
}