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Let ííc be the complementary of a bounded regular domain in R of boundary T. We consider the problem (1) l Au = f; in nc, where /has its support in a bounded subdomain nx of Í2e. Let T2 be the common boundary of fij and fi2 = f2c -ßj. We solve the problem (1) by using an equivalent system of equations involving an integral equation on r2 coupled with the equation: in il, (2) ÍAu =f «Ir = "o "lr\, = *•• r2W e introduce a finite element approximation of Eq. (2) and of the integral equation and we prove optimal error estimates.doi:10.1090/s0025-5718-1980-0583487-9 fatcat:suq6htnc7bflhdlukaqlaxlbiy