The convergence analysis and uniqueness of blow-up solutions for a Dirichlet problem of the general k-Hessian equations

Abstract In this paper, we focus on the convergence analysis of the unique solution for a Dirichlet problem of the general k -Hessian equation in a ball. By introducing some suitable growth conditions and developing a new iterative technique, the unique solution of the k -Hessian equation is obtained. Then we carry out the convergence analysis for the iterative sequences and further obtain the convergence rate and error estimate for the unique solution. The numerical result indicates that the convergence rate is very fast.

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