In this paper, we discuss a Cauchy problem for a class of nonlinear elliptic equations with data on a piece of the boundary surface. To this end, we construct a Dirichlet to Neumann operator, and provide reasonable necessary and sufficient conditions for the solvability of the problem.

nonlinear PDE, Cauchy problem, elliptic operators, variational methods, Euler equations

Received: October 25, 2024; Accepted: December 13, 2024; Published: January 16, 2025

How to cite this article: I. Ly, T. Dabre and B. Bella, Reasonable conditions for solving nonlinear elliptic Cauchy problems, International Journal of Numerical Methods and Applications 25(1) (2025), 133-150. https://doi.org/10.17654/0975045225006

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

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