2011/04/28 by Scott N. Armstrong, Boyan Sirakov, Charles K. Smart
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Boundary (topology) #Boundary value problem #Bounded function #Cone (formal languages) #Differential Equations and Boundary Problems #Gravitational singularity #Homogeneous #Lipschitz continuity #Lipschitz domain #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Nonlinear system #Physics #Pure mathematics #Singularity #math.AP #msc:35J25 #msc:35J60
paper · pdf · doi:10.1007/s00205-012-0505-8
41 pages, 2 figures
arxiv created 2011/04/28 · openalex publication_date 2012/03/30 · arxiv updated 2015/05/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of ℝn, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragmén-Lindelöf result as well as a principle of positive singularities in certain Lipschitz domains.