Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4230

 Title: Singular semilinear elliptic equations in the half-space Authors: Tintarev, Kyril Keywords: singular elliptic operatorssemilinear elliptic equationscritical exponentconvergenceconcentration compactness Issue Date: 2001 Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche Citation: Kyril Tintarev, "Singular semilinear elliptic equations in the half-space", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 33 (2001), pp. 327-337. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics33 (2001) Abstract: We show that equation $x_{N}^{q}\Delta u+u^{p-1}=0$ on the half-space $Y=\mathbf{R}^{N-1}\times\left(0,\infty\right)$ and on some of its subsets has a ground state solution for $q=N-\frac{p\left(N-2\right)}{2},\; p\;\epsilon\left(2,2*\right)$. For N $\geq$ 3 the end point cases p=2 and p=2{*} correspond to eh Hardy inequality and the limit exponent Sobolev inequality respectively. For N=2 the problem can be interpreted in terms of Laplace-Beltrami operator on the hyperbolic half-plane. URI: http://hdl.handle.net/10077/4230 ISSN: 0049-4704 MS Classification: 35J7035J2049R50 Appears in Collections: Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.33 (2001)

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