We survey old and new results about the so-called limiting Sobolev case for the embedding of the space W 1,n 0 (Ω) into suitable spaces of functions having exponential summability. In particular, we discuss a new notion of criticality with respect to attainability of the best constant in the related embedding inequalities and the connection with existence and nonexistence of solutions to boundary value problems, in which Moser’s functions cast in a new framework. Then, we prove a new version of Moser’s inequality in Zygmund spaces with respect to the full Sobolev norm and without boundary conditions.
A Moser type inequality in Zygmund spaces without boundary conditions / D. Cassani, B. Ruf, C. Tarsi (CONTEMPORARY MATHEMATICS). - In: Recent Trends in Nonlinear Partial Differential Equations II: Stationary Problems / [a cura di] J.B. Serrin, E.L. Mitidieri, V.D. Rădulescu. - [s.l] : American Mathematical Society, 2013. - ISBN 978-0-8218-9861-1. (( convegno Workshop in Honor of Patrizia Pucci's 60th Birthday -Nonlinea Partial Differential Equations- tenutosi a Perugia nel 2012.
A Moser type inequality in Zygmund spaces without boundary conditions
B. Ruf;C. Tarsi
2013
Abstract
We survey old and new results about the so-called limiting Sobolev case for the embedding of the space W 1,n 0 (Ω) into suitable spaces of functions having exponential summability. In particular, we discuss a new notion of criticality with respect to attainability of the best constant in the related embedding inequalities and the connection with existence and nonexistence of solutions to boundary value problems, in which Moser’s functions cast in a new framework. Then, we prove a new version of Moser’s inequality in Zygmund spaces with respect to the full Sobolev norm and without boundary conditions.File | Dimensione | Formato | |
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