About semilineat low dimension Bessel PDEs

Publication type:
Paper in peer-reviewed journals
assets/images/icons/icon_arxiv.png 2404.03243
Keywords :
SDEs with distributional drift; Bessel processes; Kolmogorov equation; mild and weak solutions; self-adjoint operators; Friedrichs extension.
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.
    author={Alberto Ohashi and Francesco Russo and Alan Teixeira },
    title={About semilineat low dimension Bessel PDEs },
    year={submitted },