Multiple surfaces of non-constant mean curvature

Jakobowsky, Norbert

doi:10.1007/bf02571958

Cited by 8 publications

(7 citation statements)

References 24 publications

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“…With respect to these problems, we quote [4,23] for the case H constant, and [3,15,16] when H is a perturbation of a constant. In this paper we shall prove the following result.…”

mentioning

confidence: 99%

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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“…With respect to these problems, we quote [4,23] for the case H constant, and [3,15,16] when H is a perturbation of a constant. In this paper we shall prove the following result.…”

mentioning

confidence: 99%

Weak limit and blowup of approximate solutions to H-systems

Caldiroli

Musina

2007

Journal of Functional Analysis

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“…The knowledge of the behaviour of sequences of approximate solutions for the Dirichlet problem u = 2H (u)u x ∧ u y in D, u = γ on ∂D could be helpful in the direction of the Rellich conjecture (for the case H constant see [4,[17][18][19] and the references therein; see also [2,13,14] for a nonconstant perturbative case).…”

Section: Some Perspectivesmentioning

confidence: 99%

Blow-up analysis for the prescribed mean curvature equation onR2

Caldiroli

2009

Journal of Functional Analysis

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“…While the Plateau and the Dirichlet problems has been largely studied both for H constant and for H nonconstant (see [3,4,10,12,13,14,15,16]), problem (P H ) in the case of nonconstant H has been investigated only recently, see [5,6,7]. In [5] Caldiroli and Musina proved the existence of H-bubbles with minimal energy under the assumptions that H ∈ C 1 (R 3 ) satisfies (i) sup u∈R 3 |∇H(u + ξ) · u u| < 1 for some ξ ∈ R 3 ,…”

Section: Fellimentioning

confidence: 99%