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On a boundary value problem for a p ‐Dirac equation
Author(s) -
AlYasiri Zainab R.,
Gürlebeck Klaus
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3847
Subject(s) - mathematics , green's function for the three variable laplace equation , laplace's equation , mathematical analysis , laplace transform , sobolev space , burgers' equation , integro differential equation , partial differential equation , riccati equation
The p ‐Laplace equation is a nonlinear generalization of the Laplace equation. This generalization is often used as a model 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 fixed‐point 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 © 2016 John Wiley & Sons, Ltd.