Paneitz-type operators and applications

By Z. Djadli, Emmanuel Hebey, Michel Ledoux. 2000

199 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/af393757a45b06e2e8043afeeb04e5fbd1b5ae3e

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Citations in the corpus

The Nirenberg problem and its generalizations: a unified approach (2014, unknown): “[24], Robert [69], Djadli et al.”
Q‐Curvature on a Class of Manifolds with Dimension at Least 5 (2014, background): “21) is standard, and we refer the readers to [6,20] for further details.”
On a nonlinear fourth-order elliptic equation involving the critical Sobolev exponent (2003, background): “The interest in this equation grew up from its ressemblance to some geometric equations involving Paneitz operator and widely studied in these last years (see for instance [11], [6], [9], [10], [13], [17]).”
Nonlinear biharmonic equations with negative exponents (2009, background): “Lately there are great interest on quadratic curvature invariants such as Q-curvature and σk-curvature and their associated operators, see [3,6,7,10,15] and some recent survey papers [5] and [8].”
Coercivity and Struwe's compactness for Paneitz type operators with constant coefficients (2001, methodology): “As a consequence, β ≥ 0. By Djadli, Hebey and Ledoux [ 5 ], for any e> 0, there exists Be > 0 such that for all u ∈ H 2 (M ),”
Sign of Green's function of Paneitz operators and the Q curvature (2014, background): “1 Introduction Since the fundamental work [2] in dimension 4, the Paneitz operator and associated Q curvature in dimension other than 4 (see [1, 16]) attracts much attention (see [3, 5, 6, 10– 12, 17] etc and the references therein).”
Mountain pass critical points for Paneitz-Branson operators (2002, methodology): “with the coercivity of Pg. As stated in [ 6 ],for all e> 0,there exists Be > 0 such that for all u ∈ H 2 2 (M ), � �”
A strong maximum principle for the Paneitz operator and a non-local flow for the $Q$-curvature (2014, background): “on of (1.4). Consequently, the existence theory is far less developed. Note that for (1.7) no sign condition on wis required. There are some results in special geometric settings. Djadli-Hebey-Ledoux [DHL00] studied the optimal constant in the Sobolev embedding W2,2 → Ln2−n4 when n≥ 5. As a corollar”
Multiple solutions of a critical polyharmonic equation (2004, methodology): “This operator has been introduced by Paneitz [25] for smooth 4-dimensional Riemannian manifolds and was generalized by Branson [7] to smoothN -dimensional Riemannian manifolds; see also [6] and [10] for further references and important estimates.”
PRESCRIBING A FOURTH ORDER CONFORMAL INVARIANT ON THE STANDARD SPHERE — PART I: A PERTURBATION RESULT (2001, methodology): “In this section, following a previous argument by Van der Vorst [40] (see also Djadli-Hebey-Ledoux [21]), we prove an a priori estimate for solutions some fourth order equation.”
Existence of conformal metrics on $S^n$ with prescribed fourth-order invariant (2001, background): “problem on (Sn,g 0). While the scalar curvature problem has been widely studied, (see for example the monographes [6, 20], see also [21, 22]), problem (P) concerning the Q−curvature has been faced in [16, 17, 18] for dimension n= 5,6 only. The purpose of the present paper 2 is to study (P) and prove”
Prescribing a fourth order conformal invariant on the standard sphere, Part II: blow-up analysis and applications (2001, background): “We consider the following scalar product and norm on H(2) 2 (S (6)) which is equivalent to the usual one, see [24], 〈u, v〉 = ∫”