Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients

By Emmanuel Hebey, F. Robert. 2001

88 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/53bf13433fefab614d659395c32e618e21d6b6e8

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces (2013, unknown): “Indeed, taking for simplicity u ∈ C∞0 (Rn) and U ∈ C∞0 (RN × [0,∞)) such that U(x, 0) ≡ u(x) we have (2.5) ‖u‖2L2∗ (RN ) ≤ S ∗2/2∗ ∫ RN |ξ|2s|û(ξ)|2dξ ≤ C(N, s) ∫ RN ∫ ∞ 0 |∇U |2t1−2s dx dt , which extends to a bounded trace operator Tr : H 1 0 → L2 ∗ .”
A Global Compactness type result for Palais-Smale sequences in fractional Sobolev spaces (2014, methodology): “In our opinion, the contribution of this note is twofold: we extend Struwe’s Global Compactness result for Palais-Smale sequences to any fractional Sobolev spaces Ḣs, hence establishing a tool which could be useful for further investigations in this nonlocal framework; moreover, since we derive it f”
Mountain pass critical points for Paneitz-Branson operators (2002, background): “Let β ∈ R. We say that E satisfies the (P-S) condition at the level β if for any (un) a (P-S) sequence for E in H 2 (M ) such that E(un) → β,there exists a subsequence (un) of (un) such that (un) converges strongly in H 2 2 (M ). As easily checked, this limit is then a critical point for E. The lack”
Multiple solutions of a critical polyharmonic equation (2004, background): “1) has also been proved in [19] by a different argument.”
Existence and nonexistence results for critical growth biharmonic elliptic equations (2003, background): “Related generalisations of the Struwe compactness lemma to higher order problems can be found in [1,3,11,19].”