Cauchy Formulae for Functions Analytic of Order Two on $C^1 $ Domains with Applications to Elastostatics and Hydrostatics
Jonathan Cohen · SIAM Journal on Mathematical Analysis · 1989
This paper gives Cauchy-type formulae for functions analytic of order two on $C^1 $ domains obtained from the solutions of corresponding biharmonic problems. Functions analytic of order two are shown to be potentials for the solutions of systems of linear partial differential equations in two-dimensional elastostatics and hydrostatics. When combined with Cauchy formulae, integral representations are obtained for the traction problem and the linearized Stokes problem that are valid even for $C^1 $ domains.