On the Hopf Lemma

2007/09/21 by Li, YanYan, Nirenberg, L.
#35B50 #35J15 #35J25 (Secondary) #35J70 (Primary) #35K05 #35K20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0709.3531

Abstract

The Hopf Lemma for second order elliptic operators is proved to hold in domains with C^1,α, and even less regular, boundaries. It need not hold for C¹ boundaries. Corresponding results are proved for second order parabolic operators.

Related

• A centennial of the Zaremba--Hopf--Oleinik Lemma
• Boundary regularity and Hopf lemma for nondegenerate stable operators
• Hopf-Oleinik lemma for elliptic equations in double divergence form
• Boundary Lipschitz Regularity and the Hopf Lemma on Reifenberg Domains for Fully Nonlinear Elliptic Equations
• Sharp boundary estimates for elliptic operators