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Uniqueness of minimal energy solutions for a semilinear problem involving the fractional Laplacian


Authors: Julián Fernández Bonder, Analía Silva and Juan Spedaletti
Journal: Proc. Amer. Math. Soc. 147 (2019), 2925-2936
MSC (2010): Primary 35R11, 35J60
DOI: https://doi.org/10.1090/proc/14530
Published electronically: April 9, 2019
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Abstract: In this paper we study a semilinear problem for the fractional laplacian that is the counterpart of the Neumann problems in the classical setting. We show uniqueness of minimal energy solutions for small domains.


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Julián Fernández Bonder
Affiliation: Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Instituto de Matemática Santaló (IMAS), CONICET, Pabellón I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Email: jfbonder@dm.uba.ar

Analía Silva
Affiliation: Departamento de Matemática, FCFMyN, Universidad Nacional de San Luis, Instituto de Matemática Aplicada San Luis, IMASL, CONICET, Italia avenue 1556, office 5, San Luis (5700), San Luis, Argentina
Email: acsilva@unsl.edu.ar

Juan Spedaletti
Affiliation: Departamento de Matemática, FCFMyN, Universidad Nacional de San Luis, Instituto de Matemática Aplicada San Luis, IMASL, CONICET, Italia avenue 1556, office 5, San Luis (5700), San Luis, Argentina
Email: jfspedaletti@unsl.edu.ar

DOI: https://doi.org/10.1090/proc/14530
Keywords: Fractional partial differential equations, uniqueness results
Received by editor(s): November 2, 2017
Received by editor(s) in revised form: September 5, 2018, and September 30, 2018
Published electronically: April 9, 2019
Additional Notes: The first and second authors are members of CONICET
This paper was partially supported by grants UBACyT 20020130100283BA, CONICET PIP 11220150100032CO, and ANPCyT PICT 2012-0153
Communicated by: Catherine Sulem
Article copyright: © Copyright 2019 American Mathematical Society