Fractional conformal Laplacians and fractional Yamabe problems

Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems observed in [11], we formulate fractional Yamabe problems that include the boundary Yamabe problem studied by Escobar i...

Descripción completa

Detalles Bibliográficos
Autores: González Nogueras, María del Mar|||0000-0001-8237-7642, Qing, Jie
Tipo de recurso: informe técnico
Fecha de publicación:2010
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/11402
Acceso en línea:https://hdl.handle.net/2117/11402
Access Level:acceso abierto
Palabra clave:Differential equations
Equacions diferencials
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descripción
Sumario:Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems observed in [11], we formulate fractional Yamabe problems that include the boundary Yamabe problem studied by Escobar in [15]. We observe an interesting Hopf type maximum principle together with interplays between analysis of weighted trace Sobolev inequalities and conformal structure of the underlying manifolds, which extend the phenomena displayed in the classic Yamabe problem and boundary Yamabe problem