REASONABLE CONDITIONS FOR SOLVING NONLINEAR ELLIPTIC CAUCHY PROBLEMS
Keywords:
nonlinear PDE, Cauchy problem, elliptic operators, variational methods, Euler equationsDOI:
https://doi.org/10.17654/0975045225006Abstract
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.
Received: October 25, 2024
Accepted: December 13, 2024
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