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  4. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
  5. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.49 (2017)
  6. Flat solutions of the 1-Laplacian equation
 
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Flat solutions of the 1-Laplacian equation

Orsina, Luigi
•
Ponce, Augusto C.
2017
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ISSN
0049-4704
DOI
10.13137/2464-8728/16204
http://hdl.handle.net/10077/16204
  • Article

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.
Journal
Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Part of
49 (2017)
Subjects
  • 1-Laplacian

  • degenerate elliptic e...

  • nonlinear elliptic eq...

  • nonexistence of solut...

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
Licence
http://creativecommons.org/licenses/by-nc-nd/4.0/
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04_RIMUT_OrsinaPonce.pdf

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