Abstract
Now we turn to embedding theorems for functions with unrestricted boundary values. The present chapter contains conditions on Ω that are necessary and sufficient for the embedding operator \(L^{1}_{1}(\varOmega) \to L_{q}(\varOmega)\) to be continuous or compact. These criteria are intimately connected with relative isoperimetric inequalities and isoperimetric functions. In Sect. 5.2 we consider the cases q≥1 and 0<q<1 separately.
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© 2011 Springer-Verlag Berlin Heidelberg
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Maz’ya, V. (2011). Integrability of Functions in the Space \(L^{1}_{1}(\varOmega )\) . In: Sobolev Spaces. Grundlehren der mathematischen Wissenschaften, vol 342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15564-2_5
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DOI: https://doi.org/10.1007/978-3-642-15564-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15563-5
Online ISBN: 978-3-642-15564-2
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