| Summary: | We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kind ∑i=1s∂iiu+∑i=s+1N∂i(Ai(x,u,∇u))=0,x∈Ω⊂⊂RNfor1≤s≤(N−1),\mathop{\sum }\limits_{i=1}^{s}{\partial }_{ii}u+\mathop{\sum }\limits_{i=s+1}^{N}{\partial }_{i}({A}_{i}\left(x,u,\nabla u))=0,\hspace{1.0em}x\in \Omega \subset \hspace{-0.3em}\subset \hspace{0.33em}{{\mathbb{R}}}^{N}\hspace{1.0em}\hspace{0.1em}\text{for}\hspace{0.1em}\hspace{0.33em}1\le s\le \left(N-1), where each operator Ai{A}_{i} behaves directionally as the singular pp-Laplacian, 1<p<21\lt p\lt 2. Throughout a parabolic approach to expansion of positivity we obtain the interior Hölder continuity and some integral and pointwise Harnack inequalities.
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