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Flat solutions of the 1-Laplacian equation
Orsina, Luigi
Ponce, Augusto C.
2017
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e-ISSN
2464-8728
Abstract
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.
Part of
49 (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
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
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