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Questions involving the $p$-Laplace operator $\Delta_p u=\operatorname{div}(|\nabla u|^{p-2}\nabla u)$.

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Solution of $\vec{p}-$Laplace equation

Let $\Omega \subset {\mathbb{R}^n}$ is bounded domain with smooth boundary. We consider the bvp $$ - \sum\limits_{I = 1}^n {{\partial _{{x_i}}}\left( {{{\left| {{\partial _{{x_i}}}u} \right|}^{{p_i} …