Local gradient estimates for solutions to a class of very degenerate elliptic equations

Fengping Yao; Chao Zhang; Shulin Zhou

doi:10.1080/17476933.2026.2685089

Local gradient estimates for solutions to a class of very degenerate elliptic equations

Fengping Yao^*
, Chao Zhang
, Shulin Zhou

^*Corresponding author for this work

School of Mathematics

Shanghai University
Peking University

Research output: Contribution to journal › Article › peer-review

Abstract

In this work, we mainly investigate the local gradient estimates in the setting of Lorentz spaces for weak solutions to a class of very degenerate elliptic equations, which comes from a model of traffic congestion. It is important to point out that the equations we studied have a wide degeneracy since their moduli of ellipticity vanish on the set (Formula presented.) and then behave like the classical p-Laplacian elliptic equation only on the set (Formula presented.).

Original language	English
Journal	Complex Variables and Elliptic Equations
DOIs	https://doi.org/10.1080/17476933.2026.2685089
State	Accepted/In press - 2026

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 9 Industry, Innovation, and Infrastructure

Keywords

Lorentz spaces
Very degenerate
elliptic
gradient
regularity
weak solution

Access to Document

10.1080/17476933.2026.2685089

Cite this

@article{ec29b32361b04f5eba033e2db8bb41ab,

title = "Local gradient estimates for solutions to a class of very degenerate elliptic equations",

abstract = "In this work, we mainly investigate the local gradient estimates in the setting of Lorentz spaces for weak solutions to a class of very degenerate elliptic equations, which comes from a model of traffic congestion. It is important to point out that the equations we studied have a wide degeneracy since their moduli of ellipticity vanish on the set (Formula presented.) and then behave like the classical p-Laplacian elliptic equation only on the set (Formula presented.).",

keywords = "Lorentz spaces, Very degenerate, elliptic, gradient, regularity, weak solution",

author = "Fengping Yao and Chao Zhang and Shulin Zhou",

note = "Publisher Copyright: {\textcopyright} 2026 Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2026",

doi = "10.1080/17476933.2026.2685089",

language = "英语",

journal = "Complex Variables and Elliptic Equations",

issn = "1747-6933",

publisher = "Taylor and Francis Ltd.",

}

TY - JOUR

T1 - Local gradient estimates for solutions to a class of very degenerate elliptic equations

AU - Yao, Fengping

AU - Zhang, Chao

AU - Zhou, Shulin

PY - 2026

Y1 - 2026

N2 - In this work, we mainly investigate the local gradient estimates in the setting of Lorentz spaces for weak solutions to a class of very degenerate elliptic equations, which comes from a model of traffic congestion. It is important to point out that the equations we studied have a wide degeneracy since their moduli of ellipticity vanish on the set (Formula presented.) and then behave like the classical p-Laplacian elliptic equation only on the set (Formula presented.).

AB - In this work, we mainly investigate the local gradient estimates in the setting of Lorentz spaces for weak solutions to a class of very degenerate elliptic equations, which comes from a model of traffic congestion. It is important to point out that the equations we studied have a wide degeneracy since their moduli of ellipticity vanish on the set (Formula presented.) and then behave like the classical p-Laplacian elliptic equation only on the set (Formula presented.).

KW - Lorentz spaces

KW - Very degenerate

KW - elliptic

KW - gradient

KW - regularity

KW - weak solution

UR - https://www.scopus.com/pages/publications/105043689400

U2 - 10.1080/17476933.2026.2685089

DO - 10.1080/17476933.2026.2685089

M3 - 文章

AN - SCOPUS:105043689400

SN - 1747-6933

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

ER -

Local gradient estimates for solutions to a class of very degenerate elliptic equations

Abstract

UN SDGs

Keywords

Access to Document

Other files and links

Fingerprint

Cite this