Smoothing effect for nonlinear Schrödinger equations in exterior domains

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7 Citations (Scopus)

Abstract

We consider the following nonlinear Schrödinger equations in exterior domains: i∂tu + 1 2 Δu = |u|2 u, (t,x)∈R x D, u(0, x) = π(x), x ε{lunate} D, (*) u(t, x) = 0 (or ∂u t6v = 0), (t,x)∈R x ∂D, where D={x ∈ Rn;|x|>R}, ∂D= R > 0, and v denotes the outward normal unit vector at x ε{lunate} ∂D. In this paper we prove the radially symmetric solutions of (*) have a smoothing property.

Original languageEnglish
Pages (from-to)444-458
Number of pages15
JournalJournal of Functional Analysis
Volume89
Issue number2
DOIs
Publication statusPublished - 1990 Mar 15
Externally publishedYes

ASJC Scopus subject areas

  • Analysis

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