Sharp solvability for singular SDEs
Abstract
The attracting inversesquare drift provides a prototypical counterexample to solvability of singular SDEs: if the coefficient of the drift is larger than a certain critical value, then no weak solution exists. We prove a positive result on solvability of singular SDEs where this critical value is attained from below (up to strict inequality) for the entire class of formbounded drifts. This class contains e.g. the inversesquare drift, the critical LadyzhenskayaProdiSerrin class. The proof is based on a $L^p$ variant of De Giorgi's method.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.11232
 Bibcode:
 2021arXiv211011232K
 Keywords:

 Mathematics  Probability;
 Mathematics  Analysis of PDEs