Sub-supersolution method for a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term

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2020-02-01

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In this work we study a quasilinear elliptic problem involving the 1-laplacian operator and a gradient term. The problem requires the definition of a suitable sense of solution, which allows us to show the existence of a solution in BV(Ω), having no jump part. Despite the lack of regularity of the solutions, we develop a sub-supersolution approach, together with a thorough analysis of the distributional derivative of the functions in BV(Ω).

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1-Laplacian operator, Functions of bounded variation, Sub-supersolution method

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Journal of Functional Analysis, v. 278, n. 3, 2020.

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