Local Lipschitz bounds for solutions to certain singular elliptic equations involving the one-Laplacian

In this paper we study the local Lipschitz regularity of weak solutions to certain singular elliptic equations involving one-Laplacian. Equations treated here also contains another well-behaving operator such as $$p$$ -Laplacian with $$1<p<\infty $$ . The problem is that one-Laplacian too on degenerate points, what often called a facet, which makes it difficult obtain even solutions. This difficulty overcome by making suitable approximation schemes, and avoiding analysis facet for approximated key estimate priori uniform classical regularized equations, proved Moser’s iteration. Another bounds can be obtained De Giorgi’s truncation. Proofs estimates in are rather elementary sense nonlinear potential not used at all.