Abstract
In this paper we study nonnegative solutions of
(†) |g|γHnup≤(−ΔHn)α/2u on Hn,
where Hn is the Heisenberg group; |⋅|Hn is the homogeneous norm; ΔHn is the sub-Laplacian; (p,α,γ)∈(1,∞)×(0,2)×[0,(p−1)Q); and Q=2n+2 is the homogeneous dimension of Hn. In particular, we prove that any nonnegative solution of (†) is zero if and only if p≤Q+γ/Q−α.
(†) |g|γHnup≤(−ΔHn)α/2u on Hn,
where Hn is the Heisenberg group; |⋅|Hn is the homogeneous norm; ΔHn is the sub-Laplacian; (p,α,γ)∈(1,∞)×(0,2)×[0,(p−1)Q); and Q=2n+2 is the homogeneous dimension of Hn. In particular, we prove that any nonnegative solution of (†) is zero if and only if p≤Q+γ/Q−α.
Original language | English |
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Pages (from-to) | 379-403 |
Number of pages | 25 |
Journal | Dynamics of Partial Differential Equations |
Volume | 12 |
Issue number | 4 |
DOIs | |
Publication status | Published - 10 Dec 2015 |
Keywords
- Heisenberg group
- nonnegative weak solution
- fractional sub-Laplacian