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Subelliptic variational problems. (English) Zbl 0717.49004
Summary: Using the direct method and the Moser’s process, we prove the existence and \(C^{\mu}\) regularity of stationary point for the degenerate elliptic variational problem \(I(\mu)=\int_{\Omega}F(x,u,Xu)dx\) where \(X=(X_ 1,...,X_ m)\) is a system of real smooth vector fields which satisfy the Hörmander’s condition. The assumption imposed on F(x,u,\(\xi\)) are similar to those for the elliptic case.

MSC:
49J10 Existence theories for free problems in two or more independent variables
35J20 Variational methods for second-order elliptic equations
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