We discuss the Cauchy problem for a nonlinear elliptic operator, namely for the p-Laplace operator with data on a piece  of the boundary surface. By the Cauchy problem, we mean any boundary value problem for an unknown function y in a domain  with the property that the data on  if combined with the differential equations in , allow one to determine all derivatives of y on  by means of functional equations. We use purely nonlinear methods, such as successive iterations of a Zaremba type mixed boundary value problem for the p-Laplace operator.

nonlinear PDE, Cauchy problem, variational problems, elliptic operators.

Received: August 16, 2022; Accepted: September 29, 2022; Published: November 23, 2022

How to cite this article: B. Bella, I. Ly and A. Ouedraogo, On the Cauchy problem for the p‑Laplace operator, Universal Journal of Mathematics and Mathematical Sciences 17 (2022), 67-82.  http://dx.doi.org/10.17654/2277141722012

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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