2010/08/25 by Moshe Marcus, Marcus, Moshe, Лаурент Верон +2
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP
paper · pdf · doi:10.48550/arxiv.1008.4222
To appear in Annali Scuola Normale Superiore Pisa. arXiv admin note: substantial text overlap with arXiv:0907.1006
openalex publication_date 2010/08/25 · arxiv created 2011/10/26 · arxiv updated 2011/10/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the generalized boundary value problem for nonnegative solutions of of -Δu+g(u)=0 in a bounded Lipschitz domain Ω, when g is continuous and nondecreasing. Using the harmonic measure of Ω, we define a trace in the class of outer regular Borel measures. We amphasize the case where g(u)=|u|q-1u, q>1. When Ω is (locally) a cone with vertex y, we prove sharp results of removability and characterization of singular behavior. In the general case, assuming that Ω possesses a tangent cone at every boundary point and q is subcritical, we prove an existence and uniqueness result for positive solutions with arbitrary boundary trace.