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Title: Flat solutions of the 1-Laplacian equation
Authors: Orsina, Luigi
Ponce, Augusto C.
Keywords: 1-Laplaciandegenerate elliptic equationsnonlinear elliptic equationnonexistence of solution
Issue Date: 2017
Publisher: EUT Edizioni Università di Trieste
Source: Luigi Orsina, Augusto C. Ponce, "Flat solutions of the 1-Laplacian equation", in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics", 49 (2017), Trieste, EUT Edizioni Università di Trieste, 2017, pp. 41-51
Journal: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Part of: 49 (2017)
Abstract. For every f ∈ Ln(Ω) defined in an open bounded subset Ω of Rn, we prove that a solution u ∈ W01,1 (Ω) of the 1-Laplacian equation – div (∇u / |∇u|)= f in Ω satisfies ∇u = 0 on a set of positive Lebesgue measure. The same property holds if f ∈/ Ln(Ω) has small norm in the Marcinkiewicz space of weak–Ln functions or if u is a BV minimizer of the associated energy functional. The proofs rely on Stampacchia’s truncation method.
Type: Article
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/16204
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.49 (2017)

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