2006/10/03 by Moshe Marcus, Marcus, Moshe, Лаурент Верон +2
Computer Science · Engineering · Mathematics · #31B20 #31C15 #35J67 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 35J60 #Secondary 31B15 #Stability and Controllability of Differential Equations #math.AP #msc:31B15 #msc:31B20 #msc:31C15 #msc:35J60 #msc:35J67
paper · pdf · doi:10.48550/arxiv.math/0610102
39 pages
arxiv created 2006/10/03 · openalex publication_date 2006/10/03 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
We construct the precise boundary trace of positive solutions of Δu=uq in a smooth bounded domain in RN, for q in the super-critical range q≥ (N+1)/(N-1). The construction is performed in the framework of the fine topology associated with the Bessel capacity C2/q,q' on the boundary of the domain. We prove that the boundary trace is a Borel measure (in general unbounded), which is outer regular relative to this capacity. We provide a necessary and sufficient condition for such measures to be the boundary trace of a positive solution and prove that the corresponding generalized boundary value problem is well-posed in the class of σ-moderate solutions.