On the regularity of weak solutions for ultra-parabolic equations in the divergence form
Zhang Liqun · Scientia Sinica Mathematica · 2022
In this paper, we survey some of the recent progress on the regularity of weak solutions for ultra-parabolic equations in the divergence form with rough coefficients and related studies. We first introduce and explain the background of those equations and applications in related different areas. Then we mainly talk about the new development in the study of De Giorgi-Nash-Moser regularity theory for weak solutions of ultra-parabolic equations and some of the applications of these results in related problems.