Abstract
Let n ∈ 𝜖, n ≥ 2, q ∈ (1, ∞) and let \({\Omega }\subset \mathbb {R}^{n}\) be an open bounded set. We study the Concentration-Compactness Principle for the embedding of the Lorentz-Sobolev space \({W_{0}^{1}}L^{n,q}({\Omega })\) into an Orlicz space corresponding to a Young function \(t\mapsto \exp (t^{q^{\prime }})-1\). The results are stated with respect to the (quasi-)norm
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Černý, R. Concentration-Compactness Principle for Moser-type Inequalities in Lorentz-Sobolev Spaces. Potential Anal 43, 97–126 (2015). https://doi.org/10.1007/s11118-015-9465-6
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DOI: https://doi.org/10.1007/s11118-015-9465-6
Keywords
- Sobolev spaces
- Lorentz-Sobolev spaces
- Moser-Trudinger inequality
- Concentration-Compactness principle
- Sharp constants