Some remarks on the Lp regularity of second derivatives of solutions to\n non-divergence elliptic equations and the Dini condition

2016/06/17 by Luis Escauriaza, Escauriaza, Luis, Santiago Montaner +1 · 1 citation
Mathematics · #35B65 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1606.05577

openalex publication_date 2016/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove an end-point regularity result on the Lp integrability\nof the second derivatives of solutions to non-divergence form uniformly\nelliptic equations whose second derivatives are a priori only known to be\nintegrable. The main assumption on the elliptic operator is the Dini continuity\nof the coefficients. We provide a counterexample showing that the Dini\ncondition is somehow optimal. We also give a counterexample related to the BMO\nregularity of second derivatives of solutions to elliptic equations.\n

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