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A unified approach to degenerate problems in the half-space
Giorgio Metafune, Luigi Negro, Chiara Spina
We study elliptic and parabolic problems governed by the singular elliptic operators \begin{equation*} \mathcal L =y^{α_1}Δ_{x} +y^{α_2}\left(D_{yy}+\frac{c}{y}D_y -\frac{b}{y^2}\r…
Degenerate operators on the half-line
Giorgio Metafune, Luigi Negro, Chiara Spina
We study elliptic and parabolic problems governed by the singular elliptic operators in , where $V…
Anisotropic Sobolev spaces with weights
Giorgio Metafune, Luigi Negro, Chiara Spina
We study Sobolev spaces with weights in the half-space , adapted to the singular elliptic operators \begin{equation*} \mathca…
Lp estimates for the Caffarelli-Silvestre extension operators
Giorgio Metafune, Luigi Negro, Chiara Spina
We study elliptic and parabolic problems governed by the singular elliptic operators Delta_x+c\yD_y-b\y^2 on the half-space R^{N+1}_+.
L^p estimates for Baouendi-Gru
L. Negro, G. Metafune, C. Spina
We prove L^p estimates for the Baouendi-Grushin operator L=Delta_x+|x|^αDelta_y in L^p(R^N+M), 1 < p < 1, where x belongs to R^N; y belongs to R^M. When p = 2 more general weights…
Rellich inequalities in bounded domains
G. Metafune, L. Negro, M. Sobajima +1
We find necessary and sufficient conditions for the validity of weighted Rellich inequalities in Lp for functions in bounded domains vanishing at the boundary. General operators li…