A PDE WITH DRIFT OF NEGATIVE BESOV INDEX AND LINEAR GROWTH SOLUTIONS

Elena Issoglio and Francesco Russo

submitted

Publication type:

Paper in peer-reviewed journals

HAL:

hal-03889110

arXiv:

2212.04293

Keywords :

Parabolic PDEs with linear growth distributional drift Besov spaces.Parabolic PDEs with linear growth; distributional drift.

Abstract:

This paper investigates a class of PDEs with coefficients in negative Besov spaces and whose solutions have linear growth. We show existence and uniqueness of mild and weak solutions, which are equivalent in this setting, and several continuity results. To this aim, we introduce ad-hoc Besov-H\"older type spaces that allow for linear growth, and investigate the action of the heat semigroup on them. We conclude the paper by introducing a special subclass of these spaces which has the useful property to be separable.

BibTeX:

@article{Iss-Rus-2200-1,
    author={Elena Issoglio and Francesco Russo },
    title={A PDE WITH DRIFT OF NEGATIVE BESOV INDEX AND LINEAR GROWTH 
           SOLUTIONS },
    year={submitted },
    month={12},
}