On a boundary value problem for a p-Dirac equation

摘要

The p-Laplace equation is a nonlinear generalization of the Laplace equation. This generalization is often used as amodel problem for special types of nonlinearities. The p-Laplace equation can be seen as a bridge between very general nonlinear equations and the linear Laplace equation. The aim of this paper is to solve the p-Laplace equation for 1 < p < 2 and to find strong solutions. The idea is to apply a hypercomplex integral operator and spatial function theoretic methods to transform the p-Laplace equation into the p-Dirac equation. This equation will be solved iteratively by using a fixedpoint theorem. Applying operator-theoretical methods for the p-Dirac equation and p-Laplace equation, the existence and uniqueness of solutions in certain Sobolev spaces will be proved. Copyright (C) 2016 JohnWiley & Sons, Ltd.