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