Options
Singular semilinear elliptic equations in the half-space
Tintarev, Kyril
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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
33 (2001)
Publisher
Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source
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.
Languages
en
File(s)