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Weighted Estimates on the Neumann Problem for Schr(?)dinger Equations with Lipschitz Domains

Author: HuangWenLi
Tutor: TaoXiangXing;ZhangSongYan
School: Ningbo University
Course: Basic mathematics
Keywords: Neumann problem Schr (o ¨) dinger equation Lipschitz Domains Weighted estimates
CLC: O175.29
Type: Master's thesis
Year: 2008
Downloads: 4
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Abstract


This paper considers Lipschitz region Schr (?) Dinger equation in the weighted H p ((?) Ω, ω α dσ) space and the weighted L p ((?) Ω, ω α dσ) estimates Neumann problem space , where 1 - ∈

n , n ≥ 3 is an area bounded Lipschitz connected Leaves ω α (Q) = | QQ 0 | α , where Q 0 < / sub> is the border ( ? ) on a fixed point on with non-negative singular Potential Schr (?) dinger equation -Δu Vu = 0, where V ∈ B n . we studied the boundary value at H p ((?) Ω, ω α dσ) and L p ((?) Ω, ω α dσ) of the Neumann problem . proved that when α in certain ranges , Neumann problem has a unique solution , and ( ? ) non- tangential maximal function (?) ∈ H p ((?) Ω, ω α dσ) and (?) ∈ L p ((?) Ω, ω α dσ) At the same time , we have established a consistent understanding of regularity estimates.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Partial Differential Equations > Nonlinear partial differential equations
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