A symmetry problem in potential theory
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The proof of this result is given in Section 1 ; in Section 3 we give various generalizations to elliptic differential equations other than (1). Before turning to the detailed arguments it will be of interest to discuss the physical motivation for the problem itself. Consider a viscous incompressible fluid moving in straight parallel streamlines through a straight pipe of given cross sectional form f2. If we fix rectangular coordinates in space with the z axis directed along the pipe, it is well known that the flow velocity u is then a function of x, y alone satisfying the Poisson differential equation (for n = 2) A u = A i n f2
[1] H. Weinberger,et al. Maximum principles in differential equations , 1967 .
[2] E. Hope,et al. Elementare Bemerkungen über die Lösungen partieller differentialgleichungen zweiter Ordnung vom elliptischen Typus , 1927 .
[3] I. S. Sokolnikoff. Mathematical theory of elasticity , 1946 .