We consider the Euler equation of functionals involving a term of the form
$ \int_{\Omega}(| \nabla u|^p+a(x)| \nabla u|^q) \,{ {\rm{d}}} x, $
with $ 1<p<q<p+1 $ and $ a(x)\geq 0 $. We prove weak comparison principle and summability results for the second derivatives of solutions.
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