Local Behavior
An important topic in potential theory is the study of the local behavior of harmonic functions. Perhaps the most fundamental theorem about local behavior is the regularity theorem for Laplace's equation, which states that harmonic functions are analytic. There are results which describe the local structure of level sets of harmonic functions. There is Bôcher's theorem, which characterizes the behavior of isolated singularities of positive harmonic functions. As alluded to in the last section, one can classify the isolated singularities of harmonic functions as removable singularities, poles, and essential singularities.
Read more about this topic: Potential Theory
Famous quotes containing the words local and/or behavior:
“Resorts advertised for waitresses, specifying that they “must appear in short clothes or no engagement.” Below a Gospel Guide column headed, “Where our Local Divines Will Hang Out Tomorrow,” was an account of spirited gun play at the Bon Ton. In Jeff Winney’s California Concert Hall, patrons “bucked the tiger” under the watchful eye of Kitty Crawhurst, popular “lady” gambler.”
—Administration in the State of Colo, U.S. public relief program (1935-1943)
“Gaining a better understanding of how children’s minds work at different ages will allow you to make more sense of their behaviors. With this understanding come decreased stress and increased pleasure from being a parent. It lessens the frustrations that come from expecting things that a child simply cannot do or from incorrectly interpreting a child’s behavior in adult terms.”
—Lawrence Kutner (20th century)