TY - JOUR
T1 - About semilinear low dimension Bessel PDEs
AU - Ohashi, Alberto
AU - Russo, Francesco
AU - Teixeira, Alan
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
PY - 2025/1/1
Y1 - 2025/1/1
N2 - We prove existence and uniqueness of solutions of a semilinear PDE driven by a Bessel type generator Lδ with low dimension 0<δ<1. Lδ is a local operator, whose drift component is the derivative of x↦log(|x|): in particular it is a Schwartz distribution, which is not the derivative of a continuous real function. The solutions are intended in a duality (weak) sense with respect to state space L2(R+,dμ),μ being an invariant measure for the Bessel semigroup.
AB - We prove existence and uniqueness of solutions of a semilinear PDE driven by a Bessel type generator Lδ with low dimension 0<δ<1. Lδ is a local operator, whose drift component is the derivative of x↦log(|x|): in particular it is a Schwartz distribution, which is not the derivative of a continuous real function. The solutions are intended in a duality (weak) sense with respect to state space L2(R+,dμ),μ being an invariant measure for the Bessel semigroup.
KW - Bessel processes
KW - Friedrichs extension
KW - Kolmogorov equation
KW - Mild and weak solutions
KW - SDEs with distributional drift
KW - Self-adjoint operators
UR - https://www.scopus.com/pages/publications/105014727260
U2 - 10.1007/s40072-025-00386-9
DO - 10.1007/s40072-025-00386-9
M3 - Article
AN - SCOPUS:105014727260
SN - 2194-0401
JO - Stochastics and Partial Differential Equations: Analysis and Computations
JF - Stochastics and Partial Differential Equations: Analysis and Computations
ER -