Bubbling Phenomena of Certain Palais-Smale Sequences of m-Harmonic Type Systems
نویسندگان
چکیده
In this paper, we study the bubbling phenomena of weak solution sequences of a class of degenerate quasilinear elliptic systems of m-harmonic type. We prove that, under appropriate conditions, the energy is preserved during the bubbling process. The results apply to m-harmonic maps from a manifold Ω to a homogeneous space, and to m-harmonic maps with constant volumes, and also to certain Palais-Smale sequences. §
منابع مشابه
A ug 2 00 5 Bubbling location for F - harmonic maps and Inhomogeneous Landau - Lifshitz equations ∗
Let f be a positive smooth function on a close Riemann surface (M,g). The f − energy of a map u from M to a Riemannian manifold (N, h) is defined as E f (u) = M f |∇u| 2 dV g. In this paper, we will study the blow-up properties of Palais-Smale sequences for E f. We will show that, if a Palais-Smale sequence is not compact, then it must blows up at some critical points of f. As a sequence, if an...
متن کاملBoundedness of Palais-Smale sequences associated to a fourth-order equation in conformal geometry
Under generic assumptions, we prove boundedness of Palais-Smale sequences relative to some geometric functional defined on H(M), where M is a four-dimensional manifold. Our analysis is useful to find critical points (via minimax arguments) of this functional, which give rise to conformal metrics of constant Q-curvature. The proof is based on a refined bubbling analysis, for which the main estim...
متن کاملLocating Cerami Sequences in a Mountain Pass Geometry
Let X be a real Banach space and Φ ∈ C 1 (X, R) a function with a mountain pass geometry. This ensures the existence of a Palais-Smale, and even a Cerami, sequence {u n } of approximate critical points for the mountain pass level. We obtain information about the location of such a sequence by estimating the distance of u n from S for certain types of set S as n → ∞. Under our hypotheses we can ...
متن کاملON QUASILINEAR ELLIPTIC SYSTEMS INVOLVING MULTIPLE CRITICAL EXPONENTS
In this paper, we consider the existence of a non-trivial weaksolution to a quasilinear elliptic system involving critical Hardyexponents. The main issue of the paper is to understand thebehavior of these Palais-Smale sequences. Indeed, the principaldifficulty here is that there is an asymptotic competition betweenthe energy functional carried by the critical nonlinearities. Thenby the variatio...
متن کاملMulti-layer Local Minimum Solutions of the Bistable Equation in Noncylindrical Domains
We construct local minimum solutions for the semilinear bistable equation by minimizing the corresponding functional near some approximate solutions, under the hypothesis that certain global minimum solutions are isolated. The key is a certain characterization of Palais-Smale sequences and a proof that the functional takes higher values away from the approximate solutions.
متن کامل