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This is a Quantitative Study study.

October 20, 2025Open Access

Hyperbolic Monge-Ampère Equation on a Cylinder: Well-Posedness and Stability

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The research proves the existence and uniqueness of new hodograph weak solutions while addressing corner singularities.
Key to the methodology is the hodograph transformation, converting the nonlinear equation into a linear damped wave equation.
Energy estimates established quantitative stability of rigid solutions with respect to underlying perturbations.
The study redefines rigidity-flexibility dynamics by focusing on partial convexity rather than high smoothness.

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This study analyzes the hyperbolic Monge-Ampère equation's stability in thin elastic sheets, highlighting partial convexity's role.

Deliyianni et al. (2025) studied this question.

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