Abstract
Extremals of certain variational integrals, like the one appearing in the definition II.(10.1) of the capacity, serve in connection with the theory of qr mappings as counterparts for harmonic functions in the plane. Nonlinearity enters in the theory for dimensions n ≥ 3: the Euler—Lagrange equations for such variational integrals are not linear, but only quasilinear partial differential equations. For that reason methods familiar from the classical theory are for the most part not applicable to this nonlinear potential theory.
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© 1993 Springer-Verlag Berlin Heidelberg
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Rickman, S. (1993). Variational Integrals and Quasiregular Mappings. In: Quasiregular Mappings. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78201-5_7
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DOI: https://doi.org/10.1007/978-3-642-78201-5_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-78203-9
Online ISBN: 978-3-642-78201-5
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