$L_p$-estimates for time fractional parabolic equations in divergence form with measurable coefficients

Hongjie Dong; Doyoon Kim

$L_p$-estimates for time fractional parabolic equations in divergence form with measurable coefficients

Analysis of PDEs 2019-08-20 v2

Authors: Hongjie Dong , Doyoon Kim

Abstract

In this paper, we establish $L_p$ estimates and solvability for time fractional divergence form parabolic equations in the whole space when leading coefficients are merely measurable in one spatial variable and locally have small mean oscillations with respect to the other variables. The corresponding results for equations on a half space are also derived.

Keywords

time fractional parabolic equations divergence form lp estimates measurable coefficients small mean oscillation whole space half space

Cite

@article{arxiv.1901.10465,
  title  = {$L_p$-estimates for time fractional parabolic equations in divergence form with measurable coefficients},
  author = {Hongjie Dong and Doyoon Kim},
  journal= {arXiv preprint arXiv:1901.10465},
  year   = {2019}
}

Comments

48 pages. arXiv admin note: text overlap with arXiv:1806.02635

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