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Preprints, Working Papers, ... Year : 2024

ABOUT SEMILINEAR LOW DIMENSION BESSEL PDEs

Abstract

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.
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Dates and versions

hal-04530685 , version 1 (03-04-2024)

Identifiers

  • HAL Id : hal-04530685 , version 1

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Alberto Ohashi, Francesco Russo, Alan Teixeira. ABOUT SEMILINEAR LOW DIMENSION BESSEL PDEs. 2024. ⟨hal-04530685⟩
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