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- Title
Concentration phenomena to a higher order Liouville equation.
- Authors
Hyder, Ali
- Abstract
We study blow-up and quantization phenomena for a sequence of solutions (u k) to the prescribed Q-curvature problem (- Δ) n u k = Q k e 2 n u k in Ω ⊂ R 2 n , ∫ Ω e 2 n u k d x ≤ C , under natural assumptions on Q k . It is well-known that, up to a subsequence, either (u k) is bounded in a suitable norm, or there exists β k → ∞ such that u k = β k (φ + o (1)) in Ω \ (S 1 ∪ S φ) for some non-trivial non-positive n-harmonic function φ and for a finite set S 1 , where S φ is the zero set of φ . We prove quantization of the total curvature ∫ Ω ~ Q k e 2 n u k d x on the region Ω ~ ⋐ (Ω \ S φ) .
- Subjects
EQUATIONS; CURVATURE; ORDER; HYPOTHESIS; FINITE, The
- Publication
Calculus of Variations & Partial Differential Equations, 2020, Vol 59, Issue 4, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-020-01788-4