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A regularity theorem for \(\omega\)-minimizers of integral functionals. (English) Zbl 0949.49023

From the authors’ abstract: “We prove local Hölder continuity of the \(\omega\)-minimizers of the integral functional \(\int_\Omega f(x,u,Du)\), where the Carathéodory function \(f\) satisfies the following growth condition \[ |Du|^p- b(x)|u|^\gamma- a(x)\leq f(x,u,Du)\leq L(|Du|^p+ b(x)|u|^\gamma+ a(x)), \] where \(L\geq 1\), \(1<p\leq \gamma< p^*\) and \(a(x)\), \(b(x)\) are two nonnegative functions that lie in suitable \(L^p\) spaces”.

MSC:

49N60 Regularity of solutions in optimal control
49N45 Inverse problems in optimal control
35J20 Variational methods for second-order elliptic equations
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