Boundary trace of positive solutions of supercritical semilinear elliptic equations in dihedral domains

• Moshe Marcus ^[1] ; Laurent Veron ^[2]
  1. [1] Technion – Israel Institute of Technology

     Technion – Israel Institute of Technology

     Israel

     
  2. [2] Faculté des Sciences Parc de Grandmont, Tours, France
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 15, Nº Extra 1 (Special volume), 2016, págs. 501-542
• Idioma: inglés
• Enlaces
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• Resumen

  • We study the generalized boundary value problem for (E) −∆u + |u|q−1u = 0 in a dihedral domain Ω, when q > 1 is supercritical. The value of the critical exponent can take only a finite number of values depending on the geometry of Ω. When μ is a bounded Borel measure in a k-wedge, we give necessary and sufficient conditions in order it be the boundary value of a solution of (E). We also give conditions which ensure that a boundary compact subset is removable. These conditions are expressed in terms of Bessel capacities Bs,q0 in RN−k where s depends on the characteristics of the wedge. This allows us to describe the boundary trace of a positive solution of (E).