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On the Sobolev trace Theorem for variable exponent spaces in the critical range |
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| Authors: | Julián Fernández Bonder Nicolas Saintier Analia Silva |
| Institution: | 1. IMAS-CONICET, Buenos Aires, Argentina 2. Departamento de Matemática, FCEyN-Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428, Buenos Aires, Argentina 3. Universidad Nacional General Sarmiento, Juan María Gutierrez, 1150 Los Polvorines, Pcia de Bs. As, Argentina |
| Abstract: | In this paper, we study the Sobolev trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then, we give local conditions on the exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to satisfy such conditions and therefore to ensure the existence of extremals. |
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