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Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials.

Fall, Mouhamed Moustapha; Musina, Roberta — 2011

Journal of Inequalities and Applications [electronic only]

Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds

Mouhamed Moustapha Fall; Fethi Mahmoudi — 2008

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Given a domain $Ω$ of $ℝ^{m + 1}$ and a $k$ -dimensional non-degenerate minimal submanifold $K$ of $\partial Ω$ with $1 \leq k \leq m - 1$ , we prove the existence of a family of embedded constant mean curvature hypersurfaces in $Ω$ which as their mean curvature tends to infinity concentrate along $K$ and intersecting $\partial Ω$ perpendicularly along their boundaries.

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