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Properties of harmonic functions part 1: existence and uniqueness and the zero net flux property.
Автор: William Nesse
Загружено: 2020-04-16
Просмотров: 1885
Описание:
Solutions to Laplace’s equation u(x,y) are given the special name “harmonic” functions given they are so important in mathematical physics. In this series of videos we will show many of their properties. In this first part, we present the first two, and the most primary properties: (1) that for each boundary condition on u(x,y) , there is always a harmonic function that satisfies the boundary condition, and this harmonic function is unique. (2) we then present the most important property, that the flux, defined as the negative gradient, is always net-zero on any boundary of any open set in its domain. We prove this property and present an example.
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