Boundary singularities for weak solutions of semilinear elliptic problems

2007/02/09 by Manuel del Pino, Monica Musso, del Pino, Manuel +3
Computer Science · Mathematics · #35J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.math/0702247

openalex publication_date 2007/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct positive weak solutions of a class of semilinear elliptic equation which vanish in suitable trace sense on the boundary of a given smooth bounded N-dimensional domain, but which are singular at prescribed isolated points of the boundary. Similar constructions are carried out for solutions which are singular on any given embedded submanifold of the boundary.

Citations

• Global and local behavior of positive solutions of nonlinear elliptic equations

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