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EnglishWe consider a φ-rigidity property for divergence-free vector fields in the Euclidean n-space, where φ(t) is a non-negative convex function vanishing only at t = 0. We show that this property is always satisfied in dimension n = 2, while in higher dimension it requires some further restriction on φ. In particular, we exhibit counterexamples to quadratic rigidity (i.e., when φ(t) = ct^2) in dimension n ≥ 4. The validity of the quadratic rigidity, which we prove in dimension n = 2, implies the existence of the trace of a divergence-measure vector field ξ on a H1-rectifiable set S, as soon as its weak normal trace [ξ · νS ] is maximal on S. As an application, we deduce that the graph of an extremal solution to the prescribed mean curvature equation in a weakly-regular domain becomes vertical near the boundary in a pointwise sense.
Rigidity and trace properties of divergence-measure vector fields / Leonardi, Gian Paolo; Saracco, Giorgio. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8266. - STAMPA. - 2020(2020), pp. 1-17. [10.1515/acv-2019-0094]
| Titolo: | Rigidity and trace properties of divergence-measure vector fields | |
| Autori: | Leonardi, Gian Paolo; Saracco, Giorgio | |
| Autori Unitn: | ||
| Titolo del periodico: | ADVANCES IN CALCULUS OF VARIATIONS | |
| Anno di pubblicazione: | 2020 | |
| Codice identificativo Scopus: | 2-s2.0-85079644505 | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1515/acv-2019-0094 | |
| Handle: | http://hdl.handle.net/11572/279461 | |
| Citazione: | Rigidity and trace properties of divergence-measure vector fields / Leonardi, Gian Paolo; Saracco, Giorgio. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8266. - STAMPA. - 2020(2020), pp. 1-17. [10.1515/acv-2019-0094] | |
| Appare nelle tipologie: | 03.1 Articolo su rivista (Journal article) |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| OF - Rigidity and trace properties of divergence-measure vector fields - Leonardi, Saracco.pdf | galley proofs; first online | Versione editoriale (Publisher’s layout) |  | Open Access Visualizza/Apri |
| 10.1515_acv-2019-0094 (3).pdf | Versione editoriale (Publisher’s layout) | | Open Access Visualizza/Apri |
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