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On the Sobolev embedding 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, Argentina;2. Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I (1428), Buenos Aires, Argentina;3. Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutierrez 1150, C.P. 1613, Los Polvorines, Pcia de Bs. As., Argentina |
| Abstract: | In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration–Compactness Theorem for variable exponents and an adaptation of a convexity argument due to P.L. Lions, F. Pacella and M. Tricarico. |
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