About semilinear low dimension Bessel PDEs

2024/04/04 by Ohashi, Alberto, Russo, Francesco, Teixeira, Alan
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2404.03243

Abstract

We prove existence and uniqueness of solutions of a semilinear PDE driven by a Bessel type generatorL^δ with low dimension 0 < δ< 1. L^δ is a local operator, whose drift is thederivative of x ↦ log (\vert x\vert):in particular it is a Schwartz distribution, whichis not the derivative of a continuous function.The solutions are intended in a duality (''weak'') sensewith respect to state spaceL²(ℝ₊, dμ), μ being an invariant measure for the Bessel semigroup.

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