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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 operators
semilinear elliptic equations
critical exponent
convergence
concentration 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 Mathematics
33 (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: 35J70
35J20
49R50
Appears in Collections:Rendiconti dell' Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.33 (2001)

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