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We consider the cubic defocusing nonlinear Schr¨odinger equation in the two dimensional torus. Fix s > 1. Colliander, Keel, Staffilani, Tao and Takaoka proved in [CKS+10] the existence of solutions wi...
Using eigenvalues and eigenfunctions of −Δ with homogeneous Dirichlet boundary conditions on ∂Ω, where Ω is a parallelepiped of IRn , we prove some Sobolev injections.
在0∈Ω的情况下解决了一类包含临界Sobolev-Harty指数的奇异椭圆方程解的存在性,它与0∈Ω是不同的.证明了方程所对应的变分泛函满足局部(PS)条件,得到一个广义存在性定理.
We prove an Orlicz type version of the multiplicative embedding inequality for Sobolev spaces.
In this note, a Sobolev-type inequality is proved. Applications to obtaining linear decay rates for perturbations of viscous shocks are also discussed.
This paper is a corrigendum on a paper published in an earlier volume of JIPAM, 'Lower Bounds for the Infimum of the Spectrum of the Schrodinger Operator in and the Sobolev Inequalities' published in...
Lower Bounds for the Infimum of the Spectrum of the Schrödinger Operator in $\mathbb{R}^n$ and the Sobolev Inequalities.
本文给出了一种广义周期 Besov类在周期Sobolev 空间中的$n$-宽度的弱渐近估计.
This paper deals with the asymptotic behavior ofsolutions for the nonlinear Sobolev-Galpern equations. We firstshow the existence of the global weak attractor in $H^2(\Omega)\cap H_0^1(\Omega )$ for t...

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