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Volume 1,     Number 4,     Fall 1993

 

ON THE POISSON'S EQUATION
FOR DOUBLY CONNECTED REGIONS
P.N. SHIVAKUMAR AND CHUANXIANG JI

Abstract. In this paper we discuss the solution of the Poisson's equation wxx + wyy = -P/μ, (P, μ being positive constants) for a doubly connected region D formed by two closed curves C1 and C2. The quantity R = ∫Dw dxdy which represents a physical quantity in many applications is shown to have a greater value in the case of eccentric circles than in the case of a circular annulus, assuming that the areas enclosed by C1 and C2 are held constant.

 

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