Heat Flow Inequalities with Applications to Heat Flow Optimization Problems

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 1977 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Mathematical Analysis, volume 8, pages 604-618 (issn: 0036-1410, eissn: 1095-7154,

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Authors: Acker, Andrew;

doi: 10.1137/0508048

Heat Flow Inequalities with Applications to Heat Flow Optimization Problems

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Abstract

Inequalities are derived which compare the rates of heat flow across regions with different boundaries. The inequalities form the basis for an existence and uniqueness theory for several closely related free-boundary optimization problems involving the Laplace equation.

Keywords

Variational methods applied to PDEs, Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions, Potentials and capacities on other spaces

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