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Elastic deformations of membranes and wires. (English) Zbl 1161.35416

Sonnendrücker, Eric (ed.), Three courses on partial differential equations. Berlin: Walter de Gruyter (ISBN 3-11-017958-X/pbk). IRMA Lect. Math. Theor. Phys. 4, 1-70 (2003).
The paper is concerned with study of the equilibrium position of several balls on an elastic membrane. The equilibrium position is studied from the point of view of existence, uniqueness, location. To understand the three dimensional problem, there are more cases studied: The case of one disk on an elastic wire, the case of one square on a elastic wire, the case of two disks on an elastic wire, the case of a single ball on an elastic membrane and the case of several balls on an elastic membrane. Related results can be found in J. Bemelmans, M. Chipot [Calc. Var. Partial Differential Equations 3, 447–473 (1995; Zbl 0842.49013)].
For the entire collection see [Zbl 1026.00014].

MSC:

35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
49J45 Methods involving semicontinuity and convergence; relaxation
74K05 Strings
74K15 Membranes
35Q72 Other PDE from mechanics (MSC2000)
74G65 Energy minimization in equilibrium problems in solid mechanics

Citations:

Zbl 0842.49013
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