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A class of fully nonlinear elliptic equations and related functionals. (English) Zbl 0805.35036

Summary: We study the existence of classical solutions to a class of fully nonlinear elliptic equations determined by functions of the eigenvalues of the Hessian. We also deal with the corresponding functionals and obtain, among others, an inequality analogous to the Sobolev inequality \(\| u \|_{L^{2n/(n-2)} (\Omega)} \leq C \| Du \|_{L^ 2 (\Omega)}\).

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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