On strong solutions of It\^o's equations with $D\sigma $ and $b $ in Morrey classes containing $L_{d}$

N. V. Krylov

On strong solutions of It\^o's equations with $D\sigma $ and $b $ in Morrey classes containing $L_{d}$

Probability 2022-08-19 v2 Analysis of PDEs

Authors: N. V. Krylov

Abstract

We consider It\^o uniformly nondegenerate equations with time independent coefficients, the diffusion coefficient in $W^{1}_{2+\varepsilon,loc}$ , and the drift in a Morrey class containing $L_{d}$ . We prove the unique strong solvability in the class of admissible solutions for any starting point. The result is new even if the diffusion is constant.

Keywords

Ito equations strong solutions Morrey classes uniformly nondegenerate admissible solutions drift

Cite

@article{arxiv.2111.13795,
  title  = {On strong solutions of It\^o's equations with $D\sigma $ and $b $ in Morrey classes containing $L_{d}$},
  author = {N. V. Krylov},
  journal= {arXiv preprint arXiv:2111.13795},
  year   = {2022}
}

Comments

24 pages. An important example added. arXiv admin note: text overlap with arXiv:2007.06040

Related papers

View all related →