We investigate overdetermined problems for p-Laplace and generalized Monge–Ampére equations. By using the theory of domain derivative, we find duality results and characterization of the overdetermined boundary conditions via minimization of suitable functionals with respect to the domain.

中文翻译：

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p-Laplace和广义Monge-Ampére方程的超定问题

我们研究p -Laplace方程和广义Monge-Ampére方程的超定问题。通过使用域导数理论，我们发现了对偶结果，并且通过针对该域最小化了合适的泛函来表征了超定边界条件。