Symmetry of positive solutions of an almost-critical problem in an annulus

Castorina, Daniele; Pacella, Filomena
June 2005
Calculus of Variations & Partial Differential Equations;Jun2005, Vol. 23 Issue 2, p125
Academic Journal
We consider the subcritical problemwhere A is an annulus in,,is the critical Sobolev exponent andis a small parameter. We prove that solutions of (I) which concentrate at one or two points are axially symmetric.


Related Articles

  • Young measures generated by sequences in Morrey spaces. Fey, Kyle // Calculus of Variations & Partial Differential Equations;Sep2010, Vol. 39 Issue 1/2, p183 

    Let $${\Omega\subset\mathbb{R}^n}$$ be open and bounded. For 1 ≤ p < ∞ and 0 ≤ λ < n, we give a characterization of Young measures generated by sequences of functions $${\{{\bf f}_j\}_{j=1}^\infty}$$ uniformly bounded in the Morrey space...

  • Sobolev regularity of the second biharmonic problem on a rectangle. Kar�tson, J. // Acta Mathematica Hungarica;Nov2005, Vol. 109 Issue 3, p255 

    It is proved that for any f &esin; L 2(O) the weak solution of the second biharmonic problem on a rectangle satisfies u&esin; H 4(O). The proof uses the decomposition of the problem into two Poisson equations and a general condition for H 4-regularity via the eigenvalues and eigenfunctions of...

  • Sobolev Mappings: Lipschitz Density is not an Isometric Invariant of the Target. Hajłasz, Piotr // IMRN: International Mathematics Research Notices;Jun2011, Vol. 2011 Issue 12, p2794 

    If M is a compact smooth manifold and X is a compact metric space, then the Sobolev space W1,p(M,X) is defined through an isometric embedding of X into a Banach space. We prove that the answer to the question whether Lipschitz mappings Lip (M,X) are dense in W1,p(M,X) may depend on the isometric...

  • Duality and Penalization in Optimization via an Augmented Lagrangian Function with Applications. Zhou, Y.Y.; Yang, X.Q/ // Journal of Optimization Theory & Applications;Jan2009, Vol. 140 Issue 1, p171 

    This paper aims to establish duality and exact penalization results for the primal problem of minimizing an extended real-valued function in a reflexive Banach space in terms of a valley-at-0 augmented Lagrangian function. It is shown that every weak limit point of a sequence of optimal...

  • TWO DIMENSIONAL MEAN INEQUALITIES IN CERTAIN BANACH FUNCTION SPACES. Jain, Pankaj; Verma, Daulti // Real Analysis Exchange;2008, Vol. 33 Issue 1, p125 

    Weight characterization is obtained for the Lp - Xq boundedness of the two dimensional Hardy operator (H2�)(x1, x2) = ?0x1 ?0x2 �(t1, t2) dt1, dt2. By using a limiting procedure as well as by a direct method, the corresponding boundedness of the two dimensional geometric mean operator...

  • On Local Hörmander-Beurling Spaces. Villegas, Jairo // Turkish Journal of Mathematics;2004, Vol. 28 Issue 4, p387 

    In this paper we aim to extend a result of Hörmander's, that Bp ,kloc (Ω) ⊂ Cm (Ω) if (1+|⋅|)m/k ∈ Lp′, to the setting of vector valued local Hörmander-Beurling spaces, as well as to show that the space ∩j=1∞ Bpj, kjloc (Ω, E) (1 ≤ pj...

  • Asymptotics for a sobolev type equation with a critical nonlinearity. Kaikina, E.; Naumkin, P.; Shishmarev, I. // Differential Equations;May2007, Vol. 43 Issue 5, p673 

    The article deals with the Cauchy problem for the Sobolev type equation. It investigates the asymptotic behavior of the Cauchy problem for the nonlinear Sobolev type equation. It uses the idea to derive a weighted a priori estimate for energy type solutions. Furthermore, the asymptotics of...

  • SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS. Wang Meng // Chinese Annals of Mathematics;Oct2005, Vol. 26 Issue 4, p651 

    Let M be an n dimensional complete Riemannian manifold satisfying the doubling volume property and an on-diagonal heat kernel estimate. The necessary-sufficient condition for the Sobolev inequality ∥f∥q ≤ Cn,,v,p,q(∥∇f∥p + ∥f∥p) (2 ≤ p < q <...

  • A Schr�dinger Operator with Point Interactions on Sobolev Spaces. Albeverio, Sergio; Nizhnik, Leonid // Letters in Mathematical Physics;Dec2004, Vol. 70 Issue 3, p185 

    Schr�dinger operators on Sobolev spaces are considered as new solvable models with point interactions. A simple formula for the deficiency indices of a minimal Schr�dinger operator with point interactions is given. Examples of point interactions on the space W21(3) are constructed.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics