Parabolic equations involving Bessel operators and singular integrals

Jorge J. Betancor; Marta de León-Contreras

Parabolic equations involving Bessel operators and singular integrals

Analysis of PDEs 2017-02-17 v1 Classical Analysis and ODEs Functional Analysis

Authors: Jorge J. Betancor , Marta de León-Contreras

Abstract

In this paper we consider the evolution equation $\partial_t u=\Delta_\mu u+f$ and the corresponding Cauchy problem, where $\Delta_\mu$ represents the Bessel operator $\partial_x^2+(\frac{1}{4}-\mu^2)x^{-2}$ , for every $\mu>-1$ . We establish weighted and mixed weighted Sobolev type inequalities for solutions of Bessel parabolic equations. We use singular integrals techniques in a parabolic setting.

Keywords

parabolic equations cauchy problem parabolic partial differential equations

Cite

@article{arxiv.1702.04994,
  title  = {Parabolic equations involving Bessel operators and singular integrals},
  author = {Jorge J. Betancor and Marta de León-Contreras},
  journal= {arXiv preprint arXiv:1702.04994},
  year   = {2017}
}

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