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...
| Authors: | , |
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| Format: | report |
| Publication Date: | 2010 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/11402 |
| Online Access: | https://hdl.handle.net/2117/11402 |
| Access Level: | Open access |
| Keyword: | Differential equations Equacions diferencials Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Summary: | 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 |
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