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Elliptic problems involving a diffusion operator of vectorial $p\&q$-Laplacian type
We study a broad class of anisotropic Dirichlet problems driven by the nonhomogeneous operator \[ \mathcal L_Au=-\sum_{i=1}^N\partial_i\!\left( a_i(|\partial_i u|^{p_i})|\partial_i u|^{p_i-2} \partial_i u\right), \] where the functions $a_i$ satisfy structural growth and monotonicity conditions of $
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