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Volume 5,     Number 2,     Spring 1997

 

EXPLICIT BOUNDS FOR HARMONIC FUNCTIONS
SATISFYING BOUNDARY CONDITIONS
OF MIXED TYPE
LUCIO R. BERRONE

Abstract. Problems of heat conduction in materials which may undergo phase changes motivate this paper, where an analysis of the steady state temperature is made in order to determine necessary or sufficient conditions on the data for the absence of phase changes. From a mathematical standpoint, we look for estimates for the solutions to mixed boundary value problems for the Laplace equation. With this purpose, we take advantage of two classical techniques: the computation of sub and supersolutions and the use of Green's functions.

 

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