This text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Topics include the theory of weighted variational capacity; solutions and supersolutions of equation; balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; more. 1993 edition.
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Nonlinear Potential Theory Of Degenerate Elliptic Equations
Juha Heinonen (1960 2007) was Professor of Mathematics at the University of Michigan. His principal areas of research interest included quasiconformal mappings, nonlinear potential theory, and analysis on metric spaces. He was the author of over 60 research articles, including several posthumously, and two textbooks. A member of the Finnish Academy of Science and Letters, Heinonen received the Excellence in Research Award from the University of Michigan in 1997 and gave an invited lecture at the International Congress of Mathematicians in Beijing in 2002.
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