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Mean values of subtemperatures over level surfaces of Green functions. (English) Zbl 0784.35039
Earlier, the author presented a result for subtemperatures in which the mean values are taken over level surfaces of the Green function. Thus, he established an analogue to the classical result of F. Riesz that the mean values of subharmonic functions over concentric spheres of radius $$r$$, form convex functions of the form $$\log r$$ or $$r^{2-n}$$, depending on the dimension of the space. In this paper, he provides a more elementary proof of the theorem for subtemperatures and establishes two new results on thermic majorization, one developing its properties, and the second characterizing, in terms of the mean values, subtemperatures which have thermic majorization.

##### MSC:
 35K05 Heat equation
##### Keywords:
subtemperatures; Green function; thermic majorization
Full Text:
##### References:
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