On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights

Hongjie Dong; Doyoon Kim

On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights

Analysis of PDEs 2016-12-30 v2

Authors: Hongjie Dong , Doyoon Kim

Abstract

We prove generalized Fefferman-Stein type theorems on sharp functions with $A_p$ weights in spaces of homogeneous type with either finite or infinite underlying measure. We then apply these results to establish mixed-norm weighted $L_p$ -estimates for elliptic and parabolic equations/systems with (partially) BMO coefficients in regular or irregular domains.

Keywords

L_p-estimates elliptic equations parabolic equations A_p weights Fefferman-Stein theorem BMO coefficients mixed-norm estimates homogeneous spaces

Cite

@article{arxiv.1603.07844,
  title  = {On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights},
  author = {Hongjie Dong and Doyoon Kim},
  journal= {arXiv preprint arXiv:1603.07844},
  year   = {2016}
}

Comments

A solvability result added

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