Zobrazeno 1 - 10
of 210
pro vyhledávání: '"Kenig, C."'
We study the initial value problem (IVP) associated to the semi-linear fractional Sch\"odinger equation with variable coefficients. We deduce several properties of the anisotropic fractional elliptic operator modelling the dispersion relation and use
Externí odkaz:
http://arxiv.org/abs/2411.01300
We give a new proof of the $L^2$ version of Hardy's uncertainty principle based on calculus and on its dynamical version for the heat equation. The reasonings rely on new log-convexity properties and the derivation of optimal Gaussian decay bounds fo
Externí odkaz:
http://arxiv.org/abs/1506.05670
In this paper, we provide a new means of establishing solvability of the Dirichlet problem on Lipschitz domains, with measurable data, for second order elliptic, non-symmetric divergence form operators. We show that a certain optimal Carleson measure
Externí odkaz:
http://arxiv.org/abs/1409.7131
We prove that if a solution of an equation of KdV type is bounded above by a traveling wave with an amplitude that decays faster than a given linear exponential then it must be zero. We assume no restrictions neither on the size nor in the direction
Externí odkaz:
http://arxiv.org/abs/1112.3505
We prove an optimal restriction theorem for an arbitrary homogeneous polynomial hypersurface (of degree at least 2) in R^3, with affine curvature introduced as mitigating factor.
Comment: To apppear, Trans.Amer.Math.Soc
Comment: To apppear, Trans.Amer.Math.Soc
Externí odkaz:
http://arxiv.org/abs/1108.4123
We prove unique continuation properties for solutions of the evolution Schr\"odinger equation with time dependent potentials. As an application of our method we also obtain results concerning the possible concentration profiles of blow up solutions a
Externí odkaz:
http://arxiv.org/abs/1010.1906
We give a real-variable proof of the Hardy uncertainty principle. The method is based on energy estimates for evolutions with positive viscosity, convexity properties of free waves with Gaussian decay at two different times, elliptic $L^2$-estimates
Externí odkaz:
http://arxiv.org/abs/1005.1543
We prove unique continuation properties for solutions of evolution Schr\"odinger equation with time dependent potentials. In the case of the free solution these correspond to uncertainly principles referred to as being of Morgan type. As an applicati
Externí odkaz:
http://arxiv.org/abs/0909.3287
We prove large-data local stability theorems for several spin models in two dimensions.
Externí odkaz:
http://arxiv.org/abs/0906.1312
Publikováno v:
Duke Math. J. 155, no. 1 (2010), 163-187
We give a new proof of Hardy's uncertainty principle, up to the end-point case, which is only based on calculus. The method allows us to extend Hardy's uncertainty principle to Schr\"odinger equations with non-constant coefficients. We also deduce op
Externí odkaz:
http://arxiv.org/abs/0906.0884