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Advances in Calculus of Variations

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Volume 11, Issue 4


A class of shape optimization problems for some nonlocal operators

Julián Fernández BonderORCID iD: http://orcid.org/0000-0003-1097-4776 / Antonella Ritorto / Ariel Martin Salort
Published Online: 2017-05-11 | DOI: https://doi.org/10.1515/acv-2016-0065


In this work we study a family of shape optimization problem where the state equation is given in terms of a nonlocal operator. Examples of the problems considered are monotone combinations of fractional eigenvalues. Moreover, we also analyze the transition from nonlocal to local state equations.

Keywords: Fractional partial differential equations; shape optimization

MSC 2010: 35R11; 49Q10


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About the article

Received: 2016-12-27

Revised: 2017-03-29

Accepted: 2017-04-27

Published Online: 2017-05-11

Published in Print: 2018-10-01

Funding Source: Universidad de Buenos Aires

Award identifier / Grant number: 20020130100283BA

Funding Source: Consejo Nacional de Investigaciones Científicas y Técnicas

Award identifier / Grant number: PIP 11220150100032CO

Funding Source: Agencia Nacional de Promoción Científica y Tecnológica

Award identifier / Grant number: PICT 2012-0153

The present paper was partially supported by grants UBACyT 20020130100283BA, CONICET PIP 11220150100032CO and ANPCyT PICT 2012-0153. Julián Fernández Bonder and Ariel M. Salort are members of CONICET and Antonella Ritorto is a doctoral fellow of CONICET.

Citation Information: Advances in Calculus of Variations, Volume 11, Issue 4, Pages 373–386, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2016-0065.

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