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Differentiability for minimizers of anisotropic integrals

Paola CavaliereAnna D'OttavioFrancesco LeonettiMaria Longobardi — 1998

Commentationes Mathematicae Universitatis Carolinae

We consider a function u : Ω N , Ω n , minimizing the integral Ω ( | D 1 u | 2 + + | D n - 1 u | 2 + | D n u | p ) d x , 2 ( n + 1 ) / ( n + 3 ) p < 2 , where D i u = u / x i , or some more general functional with the same behaviour; we prove the existence of second weak derivatives D ( D 1 u ) , , D ( D n - 1 u ) L 2 and D ( D n u ) L p .

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