Multiple solutions to the Plateau problem for nonconstant mean curvature

DOI10.1215/S0012-7094-94-07325-0zbMath0815.53010OpenAlexW1541523882MaRDI QIDQ1325145

Olivier Rey, Fabrice Bethuel

Publication date: 22 June 1995

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-94-07325-0

zbMATH Keywords

815Dirichlet problemprescribed mean curvaturePlateau problemMountain- Pass-LemmaPalais-Smale-Sequences

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)

Related Items

A compactness theorem for weak solutions of higher-dimensional \(H\)-systems, Existence of \(H\)-bubbles in a perturbative setting, EXISTENCE OF MINIMAL H-BUBBLES, Weak limit and blowup of approximate solutions to \(H\)-systems, Existence and multiplicity results for a weighted \(p\)-Laplace equation involving Hardy potentials and critical nonlinearities, EMBEDDED DISC-TYPE SURFACES WITH LARGE CONSTANT MEAN CURVATURE AND FREE BOUNDARIES, \(H\)-bubbles in a perturbative setting: the finite-dimensional reduction method, The Dirichlet problem for \(H\)-systems with small boundary data: blowup phenomena and nonexistence results, Existence of extremals for the Maz'ya and for the Caffarelli-Kohn-Nirenberg inequalities, Blow-up analysis for the prescribed mean curvature equation on \(\mathbb R^2\)

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