On Korn-Maxwell-Sobolev inequalities

Franz Gmeineder; Daniel Spector

doi:10.1016/j.jmaa.2021.125226

On Korn-Maxwell-Sobolev inequalities

Franz Gmeineder
, Daniel Spector^*

^*Corresponding author for this work

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

14 Citations (Scopus)

Abstract

We establish a family of inequalities that allow one to estimate the L^q-norm of a matrix-valued field by the L^q-norm of an elliptic part and the L^p-norm of the matrix-valued curl. This particularly extends previous work by NEFF et al. and, as a main novelty, is applicable in the regime p=1.

Original language	English
Article number	125226
Journal	Journal of Mathematical Analysis and Applications
Volume	502
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2021.125226
Publication status	Published - 2021 Oct 1
Externally published	Yes

Keywords

Fourier multipliers
Fractional integrals
Incompatible tensor fields
Korn's inequality
Singular integrals
Sobolev inequalities

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1016/j.jmaa.2021.125226

Cite this

@article{b9e65435c2d84fdfa82e2b7ff6e59653,

title = "On Korn-Maxwell-Sobolev inequalities",

abstract = "We establish a family of inequalities that allow one to estimate the Lq-norm of a matrix-valued field by the Lq-norm of an elliptic part and the Lp-norm of the matrix-valued curl. This particularly extends previous work by NEFF et al. and, as a main novelty, is applicable in the regime p=1.",

keywords = "Fourier multipliers, Fractional integrals, Incompatible tensor fields, Korn's inequality, Singular integrals, Sobolev inequalities",

author = "Franz Gmeineder and Daniel Spector",

note = "Publisher Copyright: {\textcopyright} 2021 The Authors",

year = "2021",

month = oct,

day = "1",

doi = "10.1016/j.jmaa.2021.125226",

language = "English",

volume = "502",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - On Korn-Maxwell-Sobolev inequalities

AU - Gmeineder, Franz

AU - Spector, Daniel

PY - 2021/10/1

Y1 - 2021/10/1

N2 - We establish a family of inequalities that allow one to estimate the Lq-norm of a matrix-valued field by the Lq-norm of an elliptic part and the Lp-norm of the matrix-valued curl. This particularly extends previous work by NEFF et al. and, as a main novelty, is applicable in the regime p=1.

AB - We establish a family of inequalities that allow one to estimate the Lq-norm of a matrix-valued field by the Lq-norm of an elliptic part and the Lp-norm of the matrix-valued curl. This particularly extends previous work by NEFF et al. and, as a main novelty, is applicable in the regime p=1.

KW - Fourier multipliers

KW - Fractional integrals

KW - Incompatible tensor fields

KW - Korn's inequality

KW - Singular integrals

KW - Sobolev inequalities

UR - https://www.scopus.com/pages/publications/85104090736

UR - https://www.scopus.com/pages/publications/85104090736#tab=citedBy

U2 - 10.1016/j.jmaa.2021.125226

DO - 10.1016/j.jmaa.2021.125226

M3 - Article

AN - SCOPUS:85104090736

SN - 0022-247X

VL - 502

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 125226

ER -

On Korn-Maxwell-Sobolev inequalities

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this