Download E-books n-Harmonic Mappings Between Annuli: The Art of Integrating Free Lagrangians (Memoirs of the American Mathematical Society) PDF

By Tadeusz Iwaniec

The primary subject matter of this paper is the variational research of homeomorphisms $h: {\mathbb X} \overset{\textnormal{\tiny{onto}}}{\longrightarrow} {\mathbb Y}$ among given domain names ${\mathbb X}, {\mathbb Y} \subset {\mathbb R}^n$. The authors search for the extremal mappings within the Sobolev area ${\mathscr W}^{1,n}({\mathbb X},{\mathbb Y})$ which reduce the power necessary ${\mathscr E}_h=\int_{{\mathbb X}} \,|\!|\, Dh(x) \,|\!|\,^n\, \textrm{d}x$. as a result of normal connections with quasiconformal mappings this $n$-harmonic replacement to the classical Dirichlet necessary (for planar domain names) has drawn the eye of researchers in Geometric functionality idea. specific research is made the following for a couple of concentric round annuli the place many unforeseen phenomena approximately minimum $n$-harmonic mappings are saw. The underlying integration of nonlinear differential types, known as loose Lagrangians, turns into really a piece of paintings.

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