Nonconvex problems of semipermeable media and related topics. (English) Zbl 0574.73015

Boundary value problems in the theory of semipermeability potentials are studied. Both interior and boundary semipermeability problems are treated. An existence theorem is established through reformulation of the problems in terms of hemivariational inequalities and a careful definition of the required regularity conditions. The proof is constructive. It is therefore directly applicable to obtaining useful approximate solutions. Explicit applications are given to corresponding problems in the theory of elasticity.
Reviewer: D.G.B.Edelen


74S30 Other numerical methods in solid mechanics (MSC2010)
49J40 Variational inequalities
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
Full Text: DOI


[1] ; , Les inéquations en mécanique et en physique, Dunod, Paris 1972.
[2] Panagiotopoulos, Mech. Res. Comm. 8 pp 335– (1981)
[3] Panagiotopoulos, Mech. Res. Comm. 9 pp 23– (1982)
[4] Convex Analysis, Princeton University Press, Princeton 1970. · Zbl 0932.90001
[5] Ungleichungsprobleme in der Mechanik, RWTH Aachen 1977.
[6] Rauch, Proc. Amer. Math. Soc. 64 pp 277– (1977)
[7] Chang, J. Math. Anal. Appl. 80 pp 102– (1981)
[8] Clarke, Trans. Amer. Math. Soc. 205 pp 247– (1975)
[9] Rockafellar, Canadian J. Math. 32 pp 257– (1980) · Zbl 0447.49009
[10] Inequality problems in mechanics and applications. The convex and the nonconvex case. Birkhäuser Verlag, Basel Boston, 1983.
[11] Nichtlineare Funktionalanalysis, B. G. Teubner, Stuttgart 1979.
[12] Quelques méthodes de résolution des problèmes aux limites nonlinéaires, Dunod-Gauthier Villars, Paris 1969.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.