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Regularity and weak comparison principles for double phase quasilinear elliptic equations

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  • 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.

    Mathematics Subject Classification: Primary: 35B05, 35B65, 35J92; Secondary: 35D10.


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