Decay and regularity for the schrödinger equation

Matania Ben-artzi; Sergiu Klainerman

doi:10.1007/BF02790356

Decay and regularity for the schrödinger equation

Matania Ben-artzi^*
, Sergiu Klainerman

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

97 Scopus citations

Abstract

Consider the Schrödinger equation {fx25-1}. The following estimates are proved: (A) If V≡0 then for any 0≤α<1/2, {fx25-2}, and for α=1/2, s>1/2, {fx25-3} (B) If |V(x)|≤C(1+|x|²)^-1-δ, δ>0, then (if 0 is neither an eigenvalue nor a resonance of -Δ+V), {fx25-4}.

Original language	English
Pages (from-to)	25-37
Number of pages	13
Journal	Journal d'Analyse Mathematique
Volume	58
Issue number	1
DOIs	https://doi.org/10.1007/BF02790356
State	Published - Dec 1992

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title = "Decay and regularity for the schr{\"o}dinger equation",

abstract = "Consider the Schr{\"o}dinger equation \{fx25-1\}. The following estimates are proved: (A) If V≡0 then for any 0≤α<1/2, \{fx25-2\}, and for α=1/2, s>1/2, \{fx25-3\} (B) If |V(x)|≤C(1+|x|2)-1-δ, δ>0, then (if 0 is neither an eigenvalue nor a resonance of -Δ+V), \{fx25-4\}.",

author = "Matania Ben-artzi and Sergiu Klainerman",

year = "1992",

month = dec,

doi = "10.1007/BF02790356",

language = "אנגלית",

volume = "58",

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journal = "Journal d'Analyse Mathematique",

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T1 - Decay and regularity for the schrödinger equation

AU - Ben-artzi, Matania

AU - Klainerman, Sergiu

PY - 1992/12

Y1 - 1992/12

N2 - Consider the Schrödinger equation {fx25-1}. The following estimates are proved: (A) If V≡0 then for any 0≤α<1/2, {fx25-2}, and for α=1/2, s>1/2, {fx25-3} (B) If |V(x)|≤C(1+|x|2)-1-δ, δ>0, then (if 0 is neither an eigenvalue nor a resonance of -Δ+V), {fx25-4}.

AB - Consider the Schrödinger equation {fx25-1}. The following estimates are proved: (A) If V≡0 then for any 0≤α<1/2, {fx25-2}, and for α=1/2, s>1/2, {fx25-3} (B) If |V(x)|≤C(1+|x|2)-1-δ, δ>0, then (if 0 is neither an eigenvalue nor a resonance of -Δ+V), {fx25-4}.

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VL - 58

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JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

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ER -

Decay and regularity for the schrödinger equation

Abstract

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