Characterizations to the fractional Sobolev inequality

Ritva Hurri-Syrjänen, Antti V. Vähäkangas

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Abstract

We characterize the fractional Sobolev inequality with the fractional isoperimetric inequalities. We study an inequality that connects the fractional capacity with the fractional perimeter of sufficiently regular sets, and we provide examples of these sets.
Original languageEnglish
Title of host publicationComplex Analysis and Dynamical Systems VII
EditorsMark L. Agranovsky, Matania Ben-Artzi, Catherine Bénéteau, Lavi Karp, Dmitry Khavinson, Simeon Reich, David Shoikhet, Gilbert Weinstein, Lawrence Zalcman
Number of pages10
Place of PublicationRhode Island, USA
PublisherAmerican Mathematical Society
Publication dateNov 2017
Pages145-154
ISBN (Print)978-1-4704-2961-4
ISBN (Electronic)978-1-4704-4256-9
DOIs
Publication statusPublished - Nov 2017
MoE publication typeA4 Article in conference proceedings
Event7th International Conference on Complex Analysis and Dynamical Systems (CA&DS VII) - Nahariya, Israel
Duration: 10 May 201515 May 2015
Conference number: 7

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society
Volume699
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Fields of Science

  • 111 Mathematics
  • Fractional Sobolev inequality
  • fractional perimeter
  • fractional isoperimetric inequality
  • fractional capacity
  • NONLOCAL MINIMAL-SURFACES

Cite this

Hurri-Syrjänen, R., & Vähäkangas, A. V. (2017). Characterizations to the fractional Sobolev inequality. In M. L. Agranovsky, M. Ben-Artzi, C. Bénéteau, L. Karp, D. Khavinson, S. Reich, D. Shoikhet, G. Weinstein, ... L. Zalcman (Eds.), Complex Analysis and Dynamical Systems VII (pp. 145-154). (Contemporary Mathematics; Vol. 699). Rhode Island, USA: American Mathematical Society. https://doi.org/10.1090/conm/699
Hurri-Syrjänen, Ritva ; Vähäkangas, Antti V. / Characterizations to the fractional Sobolev inequality. Complex Analysis and Dynamical Systems VII. editor / Mark L. Agranovsky ; Matania Ben-Artzi ; Catherine Bénéteau ; Lavi Karp ; Dmitry Khavinson ; Simeon Reich ; David Shoikhet ; Gilbert Weinstein ; Lawrence Zalcman. Rhode Island, USA : American Mathematical Society, 2017. pp. 145-154 (Contemporary Mathematics).
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keywords = "111 Mathematics, Fractional Sobolev inequality, fractional perimeter, fractional isoperimetric inequality, fractional capacity, NONLOCAL MINIMAL-SURFACES",
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Hurri-Syrjänen, R & Vähäkangas, AV 2017, Characterizations to the fractional Sobolev inequality. in ML Agranovsky, M Ben-Artzi, C Bénéteau, L Karp, D Khavinson, S Reich, D Shoikhet, G Weinstein & L Zalcman (eds), Complex Analysis and Dynamical Systems VII. Contemporary Mathematics, vol. 699, American Mathematical Society, Rhode Island, USA, pp. 145-154, 7th International Conference on Complex Analysis and Dynamical Systems (CA&DS VII), Nahariya, Israel, 10/05/2015. https://doi.org/10.1090/conm/699

Characterizations to the fractional Sobolev inequality. / Hurri-Syrjänen, Ritva; Vähäkangas, Antti V.

Complex Analysis and Dynamical Systems VII. ed. / Mark L. Agranovsky; Matania Ben-Artzi; Catherine Bénéteau; Lavi Karp; Dmitry Khavinson; Simeon Reich; David Shoikhet; Gilbert Weinstein; Lawrence Zalcman. Rhode Island, USA : American Mathematical Society, 2017. p. 145-154 (Contemporary Mathematics; Vol. 699).

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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AB - We characterize the fractional Sobolev inequality with the fractional isoperimetric inequalities. We study an inequality that connects the fractional capacity with the fractional perimeter of sufficiently regular sets, and we provide examples of these sets.

KW - 111 Mathematics

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KW - fractional isoperimetric inequality

KW - fractional capacity

KW - NONLOCAL MINIMAL-SURFACES

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M3 - Conference contribution

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PB - American Mathematical Society

CY - Rhode Island, USA

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Hurri-Syrjänen R, Vähäkangas AV. Characterizations to the fractional Sobolev inequality. In Agranovsky ML, Ben-Artzi M, Bénéteau C, Karp L, Khavinson D, Reich S, Shoikhet D, Weinstein G, Zalcman L, editors, Complex Analysis and Dynamical Systems VII. Rhode Island, USA: American Mathematical Society. 2017. p. 145-154. (Contemporary Mathematics). https://doi.org/10.1090/conm/699