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Title: | Flat solutions of the 1-Laplacian equation | Authors: | Orsina, Luigi Ponce, Augusto C. |
Keywords: | 1-Laplacian; degenerate elliptic equations; nonlinear elliptic equation; nonexistence 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: | 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 | URI: | http://hdl.handle.net/10077/16204 | 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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