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    STUDIA MATHEMATICA - Issue no. 3 / 2008  
         
  Article:   INDEX OF THE ELASTICITY OPERATOR WITH CONTACT WITHOUT FRICTION BOUNDARY CONDITIONS.

Authors:  B. BENABDERRAHMANE, B. NOUIRI, Y. BOUKHATEM. 		 
       
         
  Abstract:  In this paper, one considers a contact without friction problem for the elasticity system, using the results given by P. Grisvard and B. Benabderrahmane respectively in ([1]: Far East J.Appl. Maths., Vol.24, No.3, p.373-380, (2006) and [2]: C.R. Acad. Sci. Paris, Ser.I Math. 304(3) (1987), 71-73), one proves that the Laplace operator is injective and with closed image of codimension N in Hs(Ω)², and consequently Δ have an index which is equal to −N, where N denotes the number of the singular solutions of the considered problem. Using the above results one proves that the elasticity operator, denoted by L has an index which is equal to −2N, by basing on the Fredholm alternative. This enables us to deduce the explicitly singular solutions and to describe the singular behavior of the solutions in the polygon.  
         
     
         
         
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