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A mean value property of elliptic equations with constant coefficients
1967
Proceedings of the American Mathematical Society
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satisfies the M.V.P. (4) u(y0)/u0(yo) = I uexp(ky')dy / I u0exp(ky')dy J B(vo,r) / J B(V",r) ior each ball B(y0, r) whose closure lies in T(R). That is if and only if u satisfies the M.V.P. (2) for each £(x0, r) whose closure lies in R. Remark. A positive solution of (1) always exists if c -bAb'^0. Putting c = 0 and Mo = l we get, from Theorem 1, immediately
doi:10.1090/s0002-9939-1967-0218747-x
fatcat:mnbhrk5sxbhx7l5ehsa2xbqfki