Article ID Journal Published Year Pages File Type
8896779 Journal of Functional Analysis 2018 28 Pages PDF
Abstract
In this paper, we are concerned with the nonrelativistic limit of the following pseudo-relativistic equation with Hartree nonlinearity or power type nonlinearity(−ħ2c2Δ+m2c4−mc2)u+μu=N(u), where c denotes the speed of light. We prove that as c→∞ the ground states of this equation converges to the ground state of its nonrelativistic counterpart−ħ22mΔu+μu=N(u) with convergence rate 1/c2 in every Hs norms. Moreover, we show that this rate is optimal.
Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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