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.
Higher regularity in congested traffic dynamics / Bogelein, V.; Duzaar, F.; Giova, R.; Passarelli di Napoli, A.. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - (2022). [10.1007/s00208-022-02375-y]
Higher regularity in congested traffic dynamics
Passarelli di Napoli A.
2022
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
