Concentrated compactness

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August undefined, 2024

WebTY - JOUR AU - Lions, Pierre-Louis TI - The concentration-compactness principle in the calculus of variations. The limit case, Part I. JO - Revista Matemática Iberoamericana PY - 1985 VL - 1 IS - 1 SP - 145 EP - 201 AB - After the study made in the locally compact case for variational problems with some translation invariance, we investigate here the …

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WebAug 1, 2001 · This approach, historically called the concentration compactness principle, emerged in the 1980's from the analysis of concentration phenomena by Uhlenbeck, … Web4. Concentrated Compactness A. Variational Problems 1. Minimizers for Critical Sobolev Nonlinearities 2. Strong Convergence of Minimizing Sequences B. Concentration-Cancellation 1. Critical Gradient Growth 2. Vorticity Bounds and Euler's Equations 5. Compensated Compactness A. Direct Methods 1. Harmonie Maps into Spheres 2. artiom zabun

Concentration Compactness - De Gruyter

WebCao D M, Nontrivial solution of semilinear elliptic equations with critical exponent in ℝ 2, Commun. Partial Differ. Equ. 17 (1992) 407–435. Article Google Scholar. Lions P L, The concentrated-compactness principle in the calculus of variations. The locally compact case, part I, Ann. I.H.P. Anal. Nonlin. 1 (1984) 109–145. WebDec 17, 2012 · Our proof involves the characterization of solitary-wave solutions as minimizers of an energy functional subject to two constraints. To establish the precompactness of minimizing sequences via concentrated compactness, we establish the sub-additivity of the problem with respect to both constraint variables jointly. WebJul 1, 1984 · In particular a general principle—called concentration-compactness principle—was shown, indicating, roughly speaking, that for general classes of minimization problems with constraints in unbounded domains all minimizing sequences are relatively compact if and only if some strict subadditivity inequalities hold (while the large ... banderas cubanas

The shape of watersheds Nature Communications

Concentrated compactness

An abstract version of the concentration compactness principle

WebAbstract. We formulate the concentration-compactness principle at infinity for both subcritical and critical case. We show some applications to the existence theory of … Webeverywhere. Moreover, we show that the delta masses are concentrated in the set where q(x) is critical. 2000 Mathematics Subject Classi cation. 35J20; 35J60. Key words and phrases. Concentration-compactness principle; Variable exponent spaces. Supported by Universidad de Buenos Aires under grant X078, by ANPCyT PICT No. 2006-290 and …

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WebMar 1, 1984 · Introduction. In the Calculus of Variations or in Mathematical Physics, many minimization problems are given on unbounded domains like ℝ N for example. In general, the invariance of ℝ N by the non-compact groups of translations and dilations creates possible loss of compactness: as an illustration of these difficulties, recall that Rellich … WebSep 5, 2024 · It is not true that in every metric space, closed and bounded is equivalent to compact. There are many metric spaces where closed and bounded is not enough to …

Web2 CHAPTER 4. WEAK CONVERGENCE AND COMPACTNESS. Proof. Clearly 1 ⇒ 2 . To show that 2 ⇒ 3, we consider fk(x) = [1 1+d(x,C)] k. fk(x) is uniformly continuous and … WebRoughly speaking, the Concentration-Compactness Principle associated with (1.1), con-tainedin[11,TheoremI.6],tellsusthat,ifasequence{uk}⊂W 1,n 0 convergespointwise and weakly to some function u ∈ W1,n 0 (), and does not concentrate at one point in ,then an inequality like (1.1) holds along the sequence {uk}, with a constant larger than nω ...

WebAug 25, 2024 · Concentrated compactness usually appears when the loss of compactness is due to an invariance under a noncompact group action, whether it … http://mate.dm.uba.ar/~jfbonder/papers/FB-S.pdf

WebThe Concentration-Compactness Principle, as developed by P.-L.Lions in [9–12], is a pow-erful tool in proving existence of extremals in functional inequalities, typically of Sobolev …

WebJun 22, 2024 · The proof is based upon a compactness lemma obtained with the help of the notion of concentration function of a measure. We give various applications to problems arising in Mathematical Physics. View arti onii chan bahasa jepangWebAug 18, 2009 · Abstract: By means of the concentrated compactness method of Bahouri-Gerard and Kenig-Merle, we prove global existence and regularity for wave maps with … banderas de guatemalaWebIts simplicity and compactness recommended it immediately for communication between ship and shore and for intermarine communication generally. Indeed, mathematicians … banderas de guyanaWebABSTRACT By means of the concentrated compactness method of Bahouri-Gerard and Kenig-Merle, we prove global existence and regularity for wave maps with smooth data and large energy from 2+1 dimensions into the hyperbolic plane. The argument yields an apriori bound of the Coulomb gauged derivative components of our wave map relative to a ... arti onii chan bakaWebMar 1, 1984 · We first derive a general principle showing the equivalence between the compactness of all minimizing sequences and some strict sub-additivity conditions. The proof is based upon a compactness lemma obtained with the help of the notion of concentration function of a measure. We give various applications to problems arising in … arti on duty dalam bahasa indonesiaWebOct 5, 2010 · In this paper we extend the well-known concentration – compactness principle of P.L. Lions to the variable exponent case. We also give some applications to the existence problem for the p (x)− ... banderas dancingWeb$\newcommand{\R}{\mathbb{R}}$ I'm reading parts of the paper The Concentration-Compactness Principle in the Calculus of Variations. The Limit Case, Part 1 by P.L. Lions. I'm trying to understand the proof of Lemma 1.1, but I'm having some trouble. The hypotheses of the lemma are the following: banderas dibujadas