MathDB
Miklos Schweitzer 1972_7

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November 5, 2008
functioninequalitiesadvanced fieldsadvanced fields unsolved

Problem Statement

Let f(x,y,z) f(x,y,z) be a nonnegative harmonic function in the unit ball of R3 \mathbb{R}^3 for which the inequality f(x0,0,0)≤ε2 f(x_0,0,0) \leq \varepsilon^2 holds for some 0≤x0≤1 0\leq x_0 \leq 1 and 0<\varepsilon<(1\minus{}x_0)^2. Prove that f(x,y,z)≤ε f(x,y,z) \leq \varepsilon in the ball with center at the origin an radius (1\minus{}3\varepsilon^{1/4}). P. Turan
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