On the convergence of nonlinear Beltrami type operators
Abstract
One of the results proved is the following: if (fh ) is a sequence of K-quasiregular mappings, converging to f in L1loc , whose jacobians verify a weak integrability condition, then the solutions of Dirichlet problems for the nonlinear Laplace-Beltrami operator associated to each fh converge to the solution of the Dirichlet problem for the nonlinear Laplace-Beltrami operator associated to f.
Such result is deduced as a particular case of a more general theorem concerning nonlinear operators.
The case of K-quasiconformal functions fh is also treated.
A class of weighted Sobolev spaces associated to quasiconformal mappings is studied.
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