Denote points in ℝ^k ×R^{N - k} as pairs ξ = (x,y), and assume 2 ≤ k < N. In this paper, we study the problem -Δ v=λ|x|^{-2} v+ |x|{-b}v^{p-1} in ℝ^N, x≠ 0, ν > 0 where $p > 2, b = N - pN - 2\2 and λ ≤ (k-2\2)2, the Hardy constant. We prove existence, symmetry and breaking symmetry results.

HARDY-SOBOLEV-MAZ'YA INEQUALITIES: SYMMETRY AND BREAKING SYMMETRY OF EXTREMAL FUNCTIONS

Musina, Roberta
2009-01-01

Abstract

Denote points in ℝ^k ×R^{N - k} as pairs ξ = (x,y), and assume 2 ≤ k < N. In this paper, we study the problem -Δ v=λ|x|^{-2} v+ |x|{-b}v^{p-1} in ℝ^N, x≠ 0, ν > 0 where $p > 2, b = N - pN - 2\2 and λ ≤ (k-2\2)2, the Hardy constant. We prove existence, symmetry and breaking symmetry results.
2009
11
6
993
1007
http://www.worldscientific.com/doi/abs/10.1142/S0219199709003636?prevSearch=musina&searchHistoryKey=
Gazzini, M; Musina, Roberta
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/32282
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