2025/11/14 by Max Hallgren, Hallgren, Max, Robert Koirala +3
Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2511.11570
openalex publication_date 2025/11/14 · openalex created_date 2025/11/18 · openalex updated_date 2026/07/28
We establish new estimates for the size and structure of the nodal set \u=0\ and the singular set \u=|∇ u|=0\ of solutions u to parabolic inequalities with parabolic Lipschitz coefficients. In particular, we show that almost all of the nodal and singular sets are covered by regular parabolic Lipschitz graphs with estimates, and that both sets satisfy parabolic Minkoswki estimates depending only on a doubling quantity at a point. Many of our results are new even for the heat equation on ℝn× ℝ.