Title of article :
Weak limit and blowup of approximate
solutions to H-systems
Author/Authors :
Paolo Caldiroli، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2007
Abstract :
Let H :R3 → R be a continuous function such that H(p) → H0 ∈ R as |p| → +∞. Fixing a domain
Ω in R2 we study the behaviour of a sequence (un) of approximate solutions to the H-system
u = 2H(u)ux ∧ uy in Ω. Assuming that supp∈R3 |(H(p) − H0)p| < 1, we show that the weak limit
of the sequence (un) solves the H-system and un →u strongly in H1 apart from a countable set S made
by isolated points. Moreover, if in addition H(p) = H0 + o(1/|p|) as |p|→+∞, then in correspondence
of each point of S we prove that the sequence (un) blows either an H-bubble or an H0-sphere.
© 2007 Elsevier Inc. All rights reserved
Keywords :
H-systems , Prescribed mean curvature equation , blowup
Journal title :
Journal of Functional Analysis
Journal title :
Journal of Functional Analysis