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Functions with orthogonal Hessian. (English) Zbl 1240.35073

Summary: A Dirichlet problem for orthogonal Hessians in two dimensions is explicitly solved, by characterizing all piecewise \(C^2\) functions \(u\: \Omega \subset \mathbb {R}^2\rightarrow \mathbb {R}\) with orthogonal Hessian in terms of a property named “second order angle condition”

MSC:

35C05 Solutions to PDEs in closed form
35J25 Boundary value problems for second-order elliptic equations
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