On a fractional Nirenberg problem, part I: blow up analysis and

Nov 5, 2011 - issues are concerned: In dimension n ≥ 4, a sequence of solutions can .... Euler-Lagrange equation for a functional associated to the ...

0 downloads 7 Views 574KB Size

Recommend Documents

Sep 14, 2017 - The modulation equation terms are estimated in brute force for K ≥ K(q) large enough from (3.35): |(νKε. 2q+1 i. ,∂iMod)L2 ρr | % ∫ νKε. 2q+2.

Jan 7, 2015 - arXiv:1402.0356v3 [math.AP] 7 Jan 2015. Peak Solutions for the fractional Nirenberg problem. Yan-Hong Chen and Youquan Zheng. Abstract. In this paper, the fractional order curvature equation (−∆)γu = (1 +. εK(x))u. N+2γ. N−2γ

Jun 3, 2008 - object (i.e., has no higher self-extensions) while the corresponding ob- jects in the ... vanced Study with supports by the Ministry of Education, Japan and the Friends of the ...... uli spaces, 31–101, CRM Proc. Lecture Notes, 38 ...

Apr 1, 2015 - 2 ˜uk| ≤. C mk in Ωk. Finally, by Lemma 2.2 for any ϕ ∈ C∞ c (R3), for all sufficiently large k depending on the size of the support of ϕ,. ∣. ∣.

Apr 16, 2018 - where i, k = 1,...,n − 1 and ∆euc is the euclidean Laplacian, by (9) and (11) and since ∆eucU = 0, in variables y = δx we have. ∆˜gq Wδ,q = 1 δ.

Oct 24, 2013 - ˜u|rTi´1,Tiq P C0`rTi´1,Tiq, 9H1˘ X C1`rTi´1,Tiq, L2˘. In particular, for the canonical evolution ˜u is right-continuous at time 0, that is. limtŒ0 ˜upt,¨q “ up0,¨q with respect to 9H1. Then. Lemma 2.1. Let ˜upt,¨q be th

Nov 5, 2010 - Choose a system of distinct representatives among the free slots for the ... be significantly under-represented in the free images for a vertex.

Nov 5, 2010 - It is well-known that one can delete a small number of vertices from a regular pair .... First we remove x from whichever of these sets it was taken. Then we add to the queue ...... is a complex for every S ∈ H. We use the convention

example, graphical) and consider the rational maps V n. PN defined by S(m). Define d(m, n) to be the degree of the (closure of the) image of this map as a cycle of dimension n. These numbers are invariants of the starting matroid which, we argue, enc

Feb 21, 2018 - one application, we transfer the bandwidth theorem of Böttcher, Schacht and Taraz [9] to the rainbow setting. It would be interesting to find out ...

Apr 20, 2015 - 0 (Ω) into Lp+1(Ω). Problem (1.1) is known as the Brezis–Nirenberg problem since the first existence results for positive solutions of (1.1) were given in their celebrated paper [14]. In particular they showed that the dimension N

Aug 4, 2015 - Perera et al. [37, Proposition 3.23]. The following compactness result, proved in Perera et al. [38, Proposition 3.1], will be crucial for applying Theorem 1.2 to our functional Iλ. Proposition 1.3. Let 1 sp, and let S be as in (1.3).

Mar 30, 2015 - This permits us to perform a complete blow-up analysis of equation (6) in the spirit of Theorem 1.1, even if we do not get exactly the same dichotomy. More precisely our first main result is the following theorem. Theorem 1.2 Let (λk)

communication system design, particularly for power control, beamforming, and energy efficiency ... Electrical and Computer Engineering, University of Toronto, Toronto, ON. M5S 3G4, Canada (e-mails: {kshen ...... [15] H. P. Benson, “Solving sum of

Mar 5, 2013 - coincides in the case of blow–ups along transverse embedded loops. 1. ..... blow–up on νS with radius 0 ≤ δ + ε

Oct 12, 2017 - the following abstract critical point theorems proved in Yang and Perera (cf. [57, Theorem. 2.2]) and in Perera, Squassina, and Yang(cf. [45, Theorem 2.2]) respectively. Recall that I satisfies the Palais-Smale compactness condition at

May 23, 2017 - Lingyu Jin, Lang Li and Shaomei Fang. Department of Mathematics, South China Agricultural University,. Guangzhou 510642, P. R. China. Abstract. In this paper, we are concerned ... Fractional Laplacian, positive solution, critical Sobol

Mar 15, 2018 - [18] established existence of solutions of space-time fractional equations with ... compact support, solution to (1.3) is defined for all time and the ...

Mar 4, 2017 - lead to a system of ODE having a similar qualitative behavior. (1.3). ∂tψk = −iHkψk + Fk(Ψ,Ψ), k = 1,··· ,N. The first author was partly supported by the Japan Society for the Promotion of Science, Grant-in-. Aid for JSPS Fel

Nov 5, 2015 - where γ > 0 as before and we shall call its solutions by "blow up solutions". Note that they ... solutions to equations involving fractional powers of the Laplacian in bounded domains. Among the works, we ..... Also, the explicit formu

Dec 25, 2004 - limits when t goes to 0 which will be defined on Rm. These limits contain a trove of infor- mation about the behaviour of the original objects in ...

We refer to a number of key survey and other papers on TFE theory such as [3, 4, 8, 9, 10, 12, 30]; see also Peletier–Troy [35] as a guide to higher-order ODEs ...

Sep 14, 2017 - (T − t). 1 p−1 . Type II blow-up bubbles. Let the Joseph-Lundgren exponent ..... Pm, m ∈ N ...... wint,q + 〈z〉wint,q + (wint,q + 〈z〉wint,q)1− d.

Nov 4, 2016 - 1 Dipartimento di Matematica, Politecnico di Milano,. P.za L. da Vinci 32, I-20133 Milano, Italy ...... We think that the logical status of these inequalities has its own interest, .... It is natural is to consider an extended inequalit