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On the Dual Reciprocal Variational Approach to the Signorini‐Fichera Problem. Convex and Nonconvex Generalization
Author(s) -
Panagiotopoulos P. D.,
Haslinger J.
Publication year - 1992
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19920721008
Subject(s) - variational inequality , mathematics , uniqueness , boundary (topology) , reciprocal , dual (grammatical number) , generalization , mathematical analysis , boundary value problem , regular polygon , geometry , philosophy , linguistics , art , literature
The aim of the present paper is the study of a new variational formulation for the Signorini‐Fichera problem. It is the dual reciprocal variational formulation which gives rise to an inequality constrained minimum problem only with respect to the unknown unilateral displacements. In the present paper the dual reciprocal variational problem is formulated for general unilateral boundary conditions derived from convex or nonconvex superpotentials. We obtain boundary variational or hemivariational inequalities and we study both for the coercive and the most important semicoercive case the existence and uniqueness (if any) of the solution. To this end a new form of Korn's inequality at the boundary is applied.