Let H be a continuous function on R^3. Fixing a domain Ω in R^2 we study the behaviour of a sequence (u_n) of approximate solutions to the H-system Δu=2H(u)u_x∧u_y in Ω. Under suitable assumptions o H, we show that the weak limit of the sequence (un) solves the H-system and un→u strongly in H^1 apart from a countable set S made by isolated points. Moreover, if in addition H(p)=H_0+o(1/|p|) as |p|→+∞, H_0 a nonzero content, then in correspondence of each point of S we prove that the sequence (u_n) blows either an H-bubble or an H_0-sphere.
Weak limit and blow up of approximate solutions to H-systems
Musina, Roberta
2007-01-01
Abstract
Let H be a continuous function on R^3. Fixing a domain Ω in R^2 we study the behaviour of a sequence (u_n) of approximate solutions to the H-system Δu=2H(u)u_x∧u_y in Ω. Under suitable assumptions o H, we show that the weak limit of the sequence (un) solves the H-system and un→u strongly in H^1 apart from a countable set S made by isolated points. Moreover, if in addition H(p)=H_0+o(1/|p|) as |p|→+∞, H_0 a nonzero content, then in correspondence of each point of S we prove that the sequence (u_n) blows either an H-bubble or an H_0-sphere.File in questo prodotto:
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