Elliptic systems and quasiconformal mappings
This monograph, which includes new results, is concerned with elliptic systems of first-order partial differential equations in the plane, in which quasiconformal mappings play a crucial role, and whose solutions are generalized analytic functions of the second kind, denoted here (?,?)-solutions. This is a brilliant translation of the German edition published in the Tuebner-text series in 1982.
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Quasiconformal mappings and solutions of Beltrami systems
Elliptic systems of partial differential equations of first order in
5 other sections not shown
a.e. in G absolutely continuous adjoint affine mapping affine transformations analogous analytic functions argument principle assertion asymptotic expansion belongs Beltrami coefficient Beltrami system boundary slits Bp(D Cauchy integral formula chain rule compact conformal mapping Consequently constant continuous function corresponding definition derivatives domain G domain GeC elliptic systems equicontinuous exists extremal problems fi)-solution finite number finite RBM fundamental solution Furthermore Hence Holder continuous holds homeomorphism hydrodynamically normalized implies inverse mapping kC(p lemma Let G Let w(z let z0 lim sup locally uniform convergence Lp(G mapping of G means measurable set neighbourhood null set obtain open set point z0 pole of order Proof properties proved quasiconformal mapping r(oo removable singularity representation theorem respect schlicht mapping schlicht solution sequence supp theorem 3.2 tion variational formulae x-conformal boundary variations zero of order