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Singularities of the divergence of continuous vector fields and uniform Hausdorff estimates
Removable singularity divergence Hausdorff measure Hausdorff content Radon measure Frostman’s lemma charges strong charges
2012/6/19
We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence o...
Continuous dependence for $H^{2}$ critical nonlinear Schr鰀inger equations in high dimensions
Nonlinear Schrodinger equation Continuous dependence Cauchy problem Strichartz抯 estimates
2012/4/17
The global existence of solutions in $H^{2}$ is well known for $H^{2}$ critical nonlinear Schr\"{o}dinger equations with small initial data in high dimensions $d\geq8$. However, even though the soluti...
Continuous Dependence of Cauchy Problem For Nonlinear Schrödinger Equation in $H^{s}$
Nonlinear Schr¨odinger equation Continuous dependence
2010/12/3
We consider the Cauchy problem for the nonlinear Schr¨odinger equation i@tu + u = 1u + 2|u| u in RN, in Hs subcritical case 0 < 4 N−2s , when 0 < s < N 2 and 0 < +1, when s > N 2 . We...