Weak limit and blowup of approximate solutions to H-systems

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