TY - JOUR
T1 - Smoothing effect for nonlinear Schrödinger equations in exterior domains
AU - Hayashi, Nakao
PY - 1990/3/15
Y1 - 1990/3/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=38249020245&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38249020245&partnerID=8YFLogxK
U2 - 10.1016/0022-1236(90)90102-Q
DO - 10.1016/0022-1236(90)90102-Q
M3 - Article
AN - SCOPUS:38249020245
SN - 0022-1236
VL - 89
SP - 444
EP - 458
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -