On Palais-Smale sequences for $H$-systems: some examples

Caldiroli, Paolo; Musina, Roberta

doi:10.57262/ade/1355867620

Adv. Differential Equations

2006

DOI: 10.57262/ade/1355867620

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On Palais-Smale sequences for $H$-systems: some examples

Paolo Caldiroli¹,

Roberta Musina²

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Cited by 3 publications

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Weak limit and blowup of approximate solutions to H-systems

Caldiroli

Musina

2007

Journal of Functional Analysis

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Let H : R 3 → R be a continuous function such that H (p) → H 0 ∈ R as |p| → +∞. Fixing a domain Ω in R 2 we study the behaviour of a sequence (u n ) of approximate solutions to the H -system u = 2H (u)u x ∧ u y in Ω. Assuming that sup p∈R 3 |(H (p) − H 0 )p| < 1, we show that the weak limit of the sequence (u n ) solves the H -system and u n → 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| → +∞, 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.

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Weak limit and blowup of approximate solutions to H-systems

Caldiroli

Musina

2007

Journal of Functional Analysis

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Blow-up analysis for the prescribed mean curvature equation onR2

Caldiroli

2009

Journal of Functional Analysis

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On the non-existence of compact surfaces of genus one with prescribed, almost constant mean curvature, close to the singular limit

Caldiroli

Iacopetti

2022

Adv. Differential Equations

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On Palais-Smale sequences for $H$-systems: some examples

Cited by 3 publications

References 10 publications

Weak limit and blowup of approximate solutions to H-systems

Weak limit and blowup of approximate solutions to H-systems

Blow-up analysis for the prescribed mean curvature equation onR2

On the non-existence of compact surfaces of genus one with prescribed, almost constant mean curvature, close to the singular limit

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