2019/11/08 by Thomas H. R. O'Neill, Bin Cheng, O'Neill, Thomas +2 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Meromorphic and Entire Functions #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.1911.03120
openalex publication_date 2019/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider Monge-Amp 'ere equations with the right hand side function close\nto a constant and from a function class that is larger than any H "older class\nand smaller than the Dini-continuous class. We establish an upper bound for the\nmodulus of continuity of the solution's second derivatives. This bound depends\nexponentially on a quantity similar to but larger than the Dini semi-norm. We\nestablish explicit control on the shape of the sequence of shrinking sections,\nhence revealing the nature of such exponential dependence.\n