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The concentration compactness principle of P.-L.Lions can be formulated in terms of general Hilbert space. Further applications to Sobolev spaces are given. 1 Decomposition in dislocated weak limits. Let H be a separable Hilbert space. DEFINITION 1.1. A bounded set D of bounded linear operators on H shall be called a set of dislocations if it satisfies the… (More)

- K. Tintarev
- 2008

We show existence of minimizers for the Hardy-Sobolev-Maz’ya inequality in Rm+n \ Rn when either m > 2, n ≥ 1 or m = 1, n ≥ 3. The authors expresses their gratitude to the faculties of mathematics departments at Technion Haifa Institute of Technology, at the University of Crete and of the University of Cyprus for their hospitality. A.T. acknowledges partial… (More)

The paper studies the existence of minimizers for Rayleigh quotients μΩ = inf ∫ Ω |∇u| 2 ∫ Ω V |u| 2 , where Ω is a domain in R N , and V is a nonzero nonnegative function that may have singularities on ∂Ω. As a model for our results one can take Ω to be a Lipschitz cone and V to be the Hardy potential V (x) = 1 |x|2 . 2000 Mathematics Subject… (More)

Let a be a quadratic form associated with a Schrödinger operator L = −∇ · (A∇) + V on a domain Ω ⊂ R. If a is nonnegative on C∞ 0 (Ω), then either there is W > 0 such that ∫ W |u|2 dx ≤ a[u] for all C∞ 0 (Ω;R), or there is a sequence φk ∈ C ∞ 0 (Ω) and a function φ > 0 satisfying Lφ = 0 such that a[φk] → 0, φk → φ locally uniformly in Ω \ {x0}. This… (More)

Let Ω be a domain in Rd, d ≥ 2, and 1 < p <∞. Fix V ∈ Lloc(Ω). Consider the functional Q and its Gâteaux derivative Q′ given by Q(u) := ∫ Ω (|∇u|+V |u|)dx, 1 p Q(u) := −∇·(|∇u|∇u)+V |u|u. If Q ≥ 0 on C∞ 0 (Ω), then either there is a positive continuous function W such that ∫ W |u|p dx ≤ Q(u) for all u ∈ C∞ 0 (Ω), or there is a sequence uk ∈ C ∞ 0 (Ω) and a… (More)

Let Ω be a domain in Rd, d ≥ 2, and 1 < p < ∞. Fix V ∈ Lloc(Ω). Consider the functional Q and its Gâteaux derivative Q′ given by

- I Schindler, K Tintarev
- 2001

The paper presents an existence result for a nonlinear Schrödinger equation with magnetic potential on unbounded domains.

- Yehuda Pinchover, Achilles Tertikas, Kyril Tintarev
- 2008

In this paper we prove a sufficient condition, in terms of the behavior of a ground state of a singular p-Laplacian problem with a potential term, such that a nonzero subsolution of another such problem is also a ground state. Unlike in the linear case (p = 2), this condition involves comparison of both the functions and of their gradients. 2000 Mathematics… (More)

Let Ω be a domain in R (possibly unbounded), N ≥ 2, 1 < p <∞, and let V ∈ Lloc(Ω). Consider the energy functional QV on C∞ c (Ω) and its Gâteaux derivative QV , respectively, given by QV (u) def = 1 p ∫ Ω (|∇u| + V |u|) dx, QV (u) = div(|∇u|p−2∇u) + V |u|p−2u, for u ∈ C∞ c (Ω). Assume that QV > 0 on C∞ c (Ω) \ {0} and QV does not have a ground state (in the… (More)

- Kyril Tintarev
- 2009

The paper raises a question about the optimal critical nonlinearity for the Sobolev space in two dimensions, connected to loss of compactness, and discusses the pertinent concentration compactness framework. We study properties of the improved version of the TrudingerMoser inequality on the open unit disk B ⊂ R2, recently proved by G. Mancini and K. Sandeep… (More)