We study some generalized small Lebesgue spaces and their associated Sobolev spaces. In particular, we prove that small Lebesgue-Sobolev spaces $W^{1,(p}(Ω)$ are compactly embedded in $L^{np\over n −p} (Ω)$, $p < n$. As an application, we study variational problems involving critical exponents under multiple constraints.
Compactness, interpolation inequalities for small Lebesgue-Sobolev spaces and applications / Fiorenza, Alberto; J. M., Rakotoson. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 25:2(2005), pp. 187-203.
Compactness, interpolation inequalities for small Lebesgue-Sobolev spaces and applications
FIORENZA, ALBERTO;
2005
Abstract
We study some generalized small Lebesgue spaces and their associated Sobolev spaces. In particular, we prove that small Lebesgue-Sobolev spaces $W^{1,(p}(Ω)$ are compactly embedded in $L^{np\over n −p} (Ω)$, $p < n$. As an application, we study variational problems involving critical exponents under multiple constraints.File in questo prodotto:
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