Higher regularity in congested traffic dynamics

Bögelein V, Duzaar F, Giova R, Passarelli di Napoli A (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Mathematische Annalen Springer Verlag (Germany)

DOI: 10.1007/s00208-022-02375-y

Abstract

In this paper, we consider minimizers of integral functionals of the type F(u):=∫Ω[1p(|Du|-1)+p+f·u]dxfor p> 1 in the vectorial case of mappings u: Rn⊃ Ω → RN with N≥ 1. Assuming that f belongs to Ln+σ for some σ> 0 , we prove that H(Du) is continuous in Ω for any continuous function H: RNn→ RNn vanishing on { ξ∈ RNn: | ξ| ≤ 1 }. This extends previous results of Santambrogio and Vespri (Nonlinear Anal 73:3832–3841, 2010) when n= 2 , and Colombo and Figalli (J Math Pures Appl (9) 101(1):94–117, 2014) for n≥ 2 , to the vectorial case N≥ 1.

Authors with CRIS profile

Frank Duzaar Lehrstuhl für Partial Differential Equations

Involved external institutions

University of Naples "Parthenope" IT Italy (IT) Universität Salzburg (Paris Lodron Universität Salzburg) AT Austria (AT) Università degli Studi di Napoli Federico II IT Italy (IT)

How to cite

APA:

Bögelein, V., Duzaar, F., Giova, R., & Passarelli di Napoli, A. (2022). Higher regularity in congested traffic dynamics. Mathematische Annalen. https://doi.org/10.1007/s00208-022-02375-y

MLA:

Bögelein, Verena, et al. "Higher regularity in congested traffic dynamics." Mathematische Annalen (2022).

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