Parabolic equations with measurable coefficients

Doyoon Kim; N. V. Krylov

doi:10.1016/j.jmaa.2006.12.077

Parabolic equations with measurable coefficients

Analysis of PDEs 2015-06-26 v1

Authors: Doyoon Kim , N. V. Krylov

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Abstract

We investigate the unique solvability of second order parabolic equations in non-divergence form in $W_p^{1,2}((0,T) \times \bR^d)$ , $p \ge 2$ . The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.

Keywords

parabolic partial differential equations parabolic equations sobolev regularity of partial differential equations

Cite

@article{arxiv.math/0604124,
  title  = {Parabolic equations with measurable coefficients},
  author = {Doyoon Kim and N. V. Krylov},
  journal= {arXiv preprint arXiv:math/0604124},
  year   = {2015}
}

Comments

19 pages

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