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:
“While it may not heighten our sympathy, wit widens our horizons by its flashes, revealing remote hidden affiliations and drawing laughter from far afield; humor, in contrast, strikes up fellow feeling, and though it does not leap so much across time and space, enriches our insight into the universal in familiar things, lending it a local habitation and a name.”
—Marie Collins Swabey. Comic Laughter, ch. 5, Yale University Press (1961)
“As long as male behavior is taken to be the norm, there can be no serious questioning of male traits and behavior. A norm is by definition a standard for judging; it is not itself subject to judgment.”
—Myriam Miedzian, U.S. author. Boys Will Be Boys, ch. 1 (1991)