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Two-point mean value formulas. (English) Zbl 1450.35019

Summary: We consider the mean value theorem for the wave equation in the Euclidean space to be a starting point to produce other mean value theorems for the wave equations on a sphere and in a space. We use transformations connecting the wave equation in the Euclidean space and the wave equation in non-Euclidean spaces. Also, we prove two-point mean value formulas for elliptic equations in the Lobachevskii space and on a sphere.

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35L05 Wave equation
35J15 Second-order elliptic equations
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