Weak limit and blowup of approximate solutions to H-systems |
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Authors: | Paolo Caldiroli Roberta Musina |
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Institution: | a Dipartimento di Matematica, Università di Torino, via Carlo Alberto, 10-10123 Torino, Italy b Dipartimento di Matematica ed Informatica, Università di Udine, via delle Scienze, 206-33100 Udine, Italy |
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Abstract: | Let 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 Δu=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. |
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Keywords: | H-systems Prescribed mean curvature equation Blowup |
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