ASYMPTOTIC ESTIMATES OF SOLUTIONS OF U(T)-1 2 DELTA-U=-VERTICAL-BAR-DEL-U-VERTICAL-BAR IN R(+)XR(R)(D) D-GREATER-THAN-OR-EQUAL-TO-2/

Authors
BENACHOUR S ROYNETTE B VALLOIS P
Citation
S. Benachour et al., ASYMPTOTIC ESTIMATES OF SOLUTIONS OF U(T)-1 2 DELTA-U=-VERTICAL-BAR-DEL-U-VERTICAL-BAR IN R(+)XR(R)(D) D-GREATER-THAN-OR-EQUAL-TO-2/, Journal of functional analysis, 144(2), 1997, pp. 301-324
Citations number
13
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
Journal of functional analysis → ACNP
ISSN journal
00221236
Volume
144
Issue
2
Year of publication
1997
Pages
301 - 324
Database
ISI
SICI code
0022-1236(1997)144:2<301:AEOSOU>2.0.ZU;2-L
Abstract
We express the solution, u(mu), of u(t) -1/2 Delta u = -\del u\ in R() x R(d), d greater than or equal to 2; u(mu) (0, .) = mu through a fu nctional of a d-dimensional Bessel process, where mu is invariant by r otations and profiled. This allows us to estimate the asymptotic behav iour of parallel to u(mu)(t, .)parallel to(1) and parallel to u(mu)(t, .)parallel to(infinity) as t goes to infinity. (C) 1997 Academic Pres s.