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Article Dans Une Revue Journal of Differential Equations Année : 2010

Existence and regularity of extremal solutions for a mean-curvature equation

Résumé

We study a class of mean curvature equations −Mu=H+λup where M denotes the mean curvature operator and for p≥1. We show that there exists an extremal parameter λ∗ such that this equation admits a minimal weak solutions for all λ∈[0,λ∗], while no weak solutions exists for λ>λ∗ (weak solutions will be defined as critical points of a suitable functional). In the radially symmetric case, we then show that minimal weak solutions are classical solutions for all λ∈[0,λ∗] and that another branch of classical solutions exists in a neighborhood (λ∗−η,λ∗) of λ∗
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Dates et versions

hal-00951465 , version 1 (20-11-2018)

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Antoine Mellet, Julien Vovelle. Existence and regularity of extremal solutions for a mean-curvature equation. Journal of Differential Equations, 2010, 249 (1), pp.37-75. ⟨10.1016/j.jde.2010.03.026⟩. ⟨hal-00951465⟩
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