Fractional Sobolev spaces with variable exponents and fractional $p(x)$-Laplacians
In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we prove the existence and uniqueness of a solution for a nonlocal problem involving...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2017-11-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6068 |
| _version_ | 1797830596804739072 |
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| author | Uriel Kaufmann Julio Rossi Raul Vidal |
| author_facet | Uriel Kaufmann Julio Rossi Raul Vidal |
| author_sort | Uriel Kaufmann |
| collection | DOAJ |
| description | In this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we prove the existence and uniqueness of a solution for a nonlocal problem involving the fractional $p(x)$-Laplacian. |
| first_indexed | 2024-04-09T13:38:38Z |
| format | Article |
| id | doaj.art-addf57c3b2d647ab8d5533db24d8af5c |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:38Z |
| publishDate | 2017-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-addf57c3b2d647ab8d5533db24d8af5c2023-05-09T07:53:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752017-11-0120177611010.14232/ejqtde.2017.1.766068Fractional Sobolev spaces with variable exponents and fractional $p(x)$-LaplaciansUriel Kaufmann0Julio Rossi1Raul Vidal2University of Cordoba, Cordoba, ArgentinaDepartamento di Matematica, Universidad de Buenos Aires, ArgentinaUniversity of Cordoba, Cordoba, ArgentinaIn this article we extend the Sobolev spaces with variable exponents to include the fractional case, and we prove a compact embedding theorem of these spaces into variable exponent Lebesgue spaces. As an application we prove the existence and uniqueness of a solution for a nonlocal problem involving the fractional $p(x)$-Laplacian.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6068variable exponentssobolev spacesfractional laplacian |
| spellingShingle | Uriel Kaufmann Julio Rossi Raul Vidal Fractional Sobolev spaces with variable exponents and fractional $p(x)$-Laplacians Electronic Journal of Qualitative Theory of Differential Equations variable exponents sobolev spaces fractional laplacian |
| title | Fractional Sobolev spaces with variable exponents and fractional $p(x)$-Laplacians |
| title_full | Fractional Sobolev spaces with variable exponents and fractional $p(x)$-Laplacians |
| title_fullStr | Fractional Sobolev spaces with variable exponents and fractional $p(x)$-Laplacians |
| title_full_unstemmed | Fractional Sobolev spaces with variable exponents and fractional $p(x)$-Laplacians |
| title_short | Fractional Sobolev spaces with variable exponents and fractional $p(x)$-Laplacians |
| title_sort | fractional sobolev spaces with variable exponents and fractional p x laplacians |
| topic | variable exponents sobolev spaces fractional laplacian |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6068 |
| work_keys_str_mv | AT urielkaufmann fractionalsobolevspaceswithvariableexponentsandfractionalpxlaplacians AT juliorossi fractionalsobolevspaceswithvariableexponentsandfractionalpxlaplacians AT raulvidal fractionalsobolevspaceswithvariableexponentsandfractionalpxlaplacians |