Functions locally almost 1-harmonic

In this article we establish some theoretical results for functions in BV(Ω ) which are such that div (∇ u / |∇ u|)∈ LN (Ω). Ω denotes an open bounded set in and σ = (∇ u / |∇ u|) is such that σ · ∇ u = |∇ u| in the distributional sense. Among the results are the study of the first eigenvalue and related eigenfunctions for the 1-Laplacian operator defined as div (∇ · / |∇ · |).

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