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Square functions associated to Schrödinger operators

I. Abu-Falahah, P. R. Stinga, J. L. Torrea (2011)

Studia Mathematica

We characterize geometric properties of Banach spaces in terms of boundedness of square functions associated to general Schrödinger operators of the form ℒ = -Δ + V, where the nonnegative potential V satisfies a reverse Hölder inequality. The main idea is to sharpen the well known localization method introduced by Z. Shen. Our results can be regarded as alternative proofs of the boundedness in H¹, L p and BMO of classical ℒ-square functions.

Stability of solutions for an abstract Dirichlet problem

Marek Galewski (2004)

Annales Polonici Mathematici

We consider continuous dependence of solutions on the right hand side for a semilinear operator equation Lx = ∇G(x), where L: D(L) ⊂ Y → Y (Y a Hilbert space) is self-adjoint and positive definite and G:Y → Y is a convex functional with superquadratic growth. As applications we derive some stability results and dependence on a functional parameter for a fourth order Dirichlet problem. Applications to P.D.E. are also given.

Stability of the inverse problem in potential scattering at fixed energy

Plamen Stefanov (1990)

Annales de l'institut Fourier

We prove an estimate of the kind ∥ q 1 - q 2 ∥ L ∞ ≤ C ϕ ( ∥ A q 1 - A q 2 ∥ R , 3 / 2 - 1 / 2 ) , where A q i ( ω , θ ) , i = 1 , 2 is the scattering amplitude related to the compactly supported potential q i ( x ) at a fixed energy level k = const., ϕ ( t ) = ( - ln t ) - δ , 0 < δ < 1 and ∥ · ∥ R , 3 / 2 - 1 / 2 is a suitably defined norm.

Stability of the Pohožaev obstrucion in dimension 3

Olivier Druet, Paul Laurain (2010)

Journal of the European Mathematical Society

We investigate problems connected to the stability of the well-known Pohoˇzaev obstruction. We generalize results which were obtained in the minimizing setting by Brezis and Nirenberg [2] and more recently in the radial situation by Brezis and Willem [3].

Stability results for Harnack inequalities

Alexander Grigor'yan, Laurent Saloff-Coste (2005)

Annales de l’institut Fourier

We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Harnack inequalities to hold on complete non-compact manifolds having non-negative Ricci curvature outside a compact set and a finite first Betti number or just having asymptotically...

Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth

Bruno Nazaret (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This article is devoted to the study of a perturbation with a viscosity term in an elliptic equation involving the p-Laplacian operator and related to the best contant problem in Sobolev inequalities in the critical case. We prove first that this problem, together with the equation, is stable under this perturbation, assuming some conditions on the datas. In the next section, we show that the zero solution is strongly isolated in some sense, among the space of the solutions. Actually, we end the...

Stabilization of Galerkin approximations of transport equations by subgrid modeling

Jean-Luc Guermond (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper presents a stabilization technique for approximating transport equations. The key idea consists in introducing an artificial diffusion based on a two-level decomposition of the approximation space. The technique is proved to have stability and convergence properties that are similar to that of the streamline diffusion method.

Currently displaying 361 – 380 of 551