Higher integrability and stability of (p,q)-quasiminimizers

Antonella Nastasi; Cintia Pacchiano Camacho

doi:10.1016/j.jde.2022.09.031

Higher integrability and stability of (p,q)-quasiminimizers

Antonella Nastasi^*
, Cintia Pacchiano Camacho

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

University of Palermo

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

4 Citations (Scopus)

Abstract

Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a (p,q)-Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian space. We also obtain a stability property with respect to the varying exponents p and q. The setting is a doubling metric measure space supporting a Poincaré inequality.

Original language	English
Pages (from-to)	121-149
Number of pages	29
Journal	Journal of Differential Equations
Volume	342
Early online date	6 Oct 2022
DOIs	https://doi.org/10.1016/j.jde.2022.09.031
Publication status	Published - 5 Jan 2023
MoE publication type	A1 Journal article-refereed

Funding

A. Nastasi is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). A. Nastasi was partly supported by GNAMPA-INdAM Project 2022 “Equazioni differenziali alle derivate parziali in fenomeni non lineari”.C. Pacchiano Camacho was supported by a doctoral training grant for 2021 from the Väisälä Fund. A. Nastasi is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). A. Nastasi was partly supported by GNAMPA-INdAM Project 2022 “Equazioni differenziali alle derivate parziali in fenomeni non lineari”.

Keywords

(p,q)-Laplace operator
Measure metric spaces
Minimal p-weak upper gradient
Minimizer

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10.1016/j.jde.2022.09.031

https://arxiv.org/abs/2203.07699

Cite this

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title = "Higher integrability and stability of (p,q)-quasiminimizers",

abstract = "Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a (p,q)-Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian space. We also obtain a stability property with respect to the varying exponents p and q. The setting is a doubling metric measure space supporting a Poincar{\'e} inequality.",

keywords = "(p,q)-Laplace operator, Measure metric spaces, Minimal p-weak upper gradient, Minimizer",

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N2 - Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a (p,q)-Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian space. We also obtain a stability property with respect to the varying exponents p and q. The setting is a doubling metric measure space supporting a Poincaré inequality.

AB - Using purely variational methods, we prove local and global higher integrability results for upper gradients of quasiminimizers of a (p,q)-Dirichlet integral with fixed boundary data, assuming it belongs to a slightly better Newtonian space. We also obtain a stability property with respect to the varying exponents p and q. The setting is a doubling metric measure space supporting a Poincaré inequality.

KW - (p,q)-Laplace operator

KW - Measure metric spaces

KW - Minimal p-weak upper gradient

KW - Minimizer

UR - https://www.scopus.com/pages/publications/85139325567

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AN - SCOPUS:85139325567

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SP - 121

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Higher integrability and stability of (p,q)-quasiminimizers

Abstract

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Keywords

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