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Fractional conformal Laplacians and fractional Yamabe problems
González Nogueras, María del Mar; Qing, Jie
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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
Àrees temàtiques de la UPC::Matemàtiques i estadística
Differential equations
Equacions diferencials
Attribution-NonCommercial-NoDerivs 3.0 Spain
Article - Draft

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