Spikes in two coupled nonlinear Schrödinger equations
Spline collocation for strongly elliptic equations on the torus.
Square functions associated to Schrödinger operators
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, and BMO of classical ℒ-square functions.
Stability estimates of an inverse problem for the stationary transport equation
Stability for semilinear parabolic equations with decaying potentials in Rn and dynamical approach to the existence of ground states
Stability in Obstacle Problems.
Stability of a numerical method for solving the 3 D inverse scattering problem with fixed energy data.
Stability of quasi-linear differential equations with transition conditions.
Stability of solutions for an abstract Dirichlet problem
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
We prove an estimate of the kind , where , is the scattering amplitude related to the compactly supported potential at a fixed energy level const., , and is a suitably defined norm.
Stability of the Pohožaev obstrucion in dimension 3
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 of the principal eigenvalue of a nonlinear elliptic system.
Stability of travelling waves in a model for conical flames in two space dimensions
Stability properties for quasilinear parabolic equations with measure data
Stability results for Harnack inequalities
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 -laplacian with critical Sobolev growth
Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth
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
Stabilization of Galerkin approximations of transport equations by subgrid modeling
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.
Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions.