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...
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| Published in | Electronic journal of qualitative theory of differential equations Vol. 2017; no. 76; pp. 1 - 10 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
University of Szeged
01.01.2017
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1417-3875 1417-3875 |
| DOI | 10.14232/ejqtde.2017.1.76 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Kaufmann, Uriel Rossi, Julio Vidal, Raul |
| Author_xml | – sequence: 1 givenname: Uriel surname: Kaufmann fullname: Kaufmann, Uriel – sequence: 2 givenname: Julio orcidid: 0000-0002-5905-4412 surname: Rossi fullname: Rossi, Julio – sequence: 3 givenname: Raul surname: Vidal fullname: Vidal, Raul |
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| Title | Fractional Sobolev spaces with variable exponents and fractional p ( x ) -Laplacians |
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