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:
“The difference between de jure and de facto segregation is the difference open, forthright bigotry and the shamefaced kind that works through unwritten agreements between real estate dealers, school officials, and local politicians.”
—Shirley Chisholm (b. 1924)
“School success is not predicted by a child’s fund of facts or a precocious ability to read as much as by emotional and social measures; being self-assured and interested: knowing what kind of behavior is expected and how to rein in the impulse to misbehave; being able to wait, to follow directions, and to turn to teachers for help; and expressing needs while getting along with other children.”
—Daniel Goleman (20th century)