Conductor sobolev-type estimates and isocapacitary inequalities

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Conductor sobolev-type estimates and isocapacitary inequalities. / Cerdà, Joan; Martín, Joaquim; Silvestre, Pilar.

julkaisussa: Indiana University Mathematics Journal, Vuosikerta 61, Nro 5, 2012, s. 1925-1947.

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

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Cerdà, J, Martín, J & Silvestre, P 2012, 'Conductor sobolev-type estimates and isocapacitary inequalities' Indiana University Mathematics Journal, Vuosikerta. 61, Nro 5, Sivut 1925-1947. DOI: 10.1512/iumj.2012.61.4709

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Cerdà, Joan ; Martín, Joaquim ; Silvestre, Pilar. / Conductor sobolev-type estimates and isocapacitary inequalities. Julkaisussa: Indiana University Mathematics Journal. 2012 ; Vuosikerta 61, Nro 5. Sivut 1925-1947

Bibtex - Lataa

@article{472778ca9e434ccebe8537f6952c00c5,
title = "Conductor sobolev-type estimates and isocapacitary inequalities",
abstract = "In this paper we present an integral inequality connecting a function space (quasi-)norm of the gradient of a function to an integral of the corresponding capacity of the conductor between two level surfaces of the function, which extends the estimates obtained by V. Maz'ya and S. Costea, and sharp capacitary inequalities due to V. Maz'ya in the case of the Sobolev norm. The inequality, obtained under appropriate convexity conditions on the function space, gives a characterization of Sobolev-type inequalities involving two measures, necessary and sufficient conditions for Sobolev isocapacitary-type inequalities, and self-improvements for integrability of Lipschitz functions.",
keywords = "Convexity, Lower estimates, Rearrangement invariant spaces, Sobolev spaces, Sobolev-type inequalities",
author = "Joan Cerd{\`a} and Joaquim Mart{\'i}n and Pilar Silvestre",
year = "2012",
doi = "10.1512/iumj.2012.61.4709",
language = "English",
volume = "61",
pages = "1925--1947",
journal = "Indiana University Mathematics Journal",
issn = "0022-2518",
publisher = "Indiana University",
number = "5",

}

RIS - Lataa

TY - JOUR

T1 - Conductor sobolev-type estimates and isocapacitary inequalities

AU - Cerdà,Joan

AU - Martín,Joaquim

AU - Silvestre,Pilar

PY - 2012

Y1 - 2012

N2 - In this paper we present an integral inequality connecting a function space (quasi-)norm of the gradient of a function to an integral of the corresponding capacity of the conductor between two level surfaces of the function, which extends the estimates obtained by V. Maz'ya and S. Costea, and sharp capacitary inequalities due to V. Maz'ya in the case of the Sobolev norm. The inequality, obtained under appropriate convexity conditions on the function space, gives a characterization of Sobolev-type inequalities involving two measures, necessary and sufficient conditions for Sobolev isocapacitary-type inequalities, and self-improvements for integrability of Lipschitz functions.

AB - In this paper we present an integral inequality connecting a function space (quasi-)norm of the gradient of a function to an integral of the corresponding capacity of the conductor between two level surfaces of the function, which extends the estimates obtained by V. Maz'ya and S. Costea, and sharp capacitary inequalities due to V. Maz'ya in the case of the Sobolev norm. The inequality, obtained under appropriate convexity conditions on the function space, gives a characterization of Sobolev-type inequalities involving two measures, necessary and sufficient conditions for Sobolev isocapacitary-type inequalities, and self-improvements for integrability of Lipschitz functions.

KW - Convexity

KW - Lower estimates

KW - Rearrangement invariant spaces

KW - Sobolev spaces

KW - Sobolev-type inequalities

UR - http://www.scopus.com/inward/record.url?scp=84888073982&partnerID=8YFLogxK

U2 - 10.1512/iumj.2012.61.4709

DO - 10.1512/iumj.2012.61.4709

M3 - Article

VL - 61

SP - 1925

EP - 1947

JO - Indiana University Mathematics Journal

T2 - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 5

ER -

ID: 17720459