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A minimization problem arising from prescribing scalar curvature functions. (English) Zbl 0855.35043

Summary: We study an extremal problem for the Dirichlet integral with a constraint arising from prescribing scalar curvature functions on a bounded smooth Euclidean domain. We can prescribe positive scalar curvature function up to a positive factor. Because the boundary values are fixed, one can only hope to find a minimizer for some specific classes of scalar curvature functions. We exhibit here one such class of functions.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
35J20 Variational methods for second-order elliptic equations
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
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References:

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