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Keywords:
Orlicz space; Orlicz-Sobolev space; embedding theorem; sharp constant; Moser-Trudinger inequality; concentration-compactness principle
Orlicz space; Orlicz-Sobolev space; embedding theorem; sharp constant; Moser-Trudinger inequality; concentration-compactness principle
Summary:
We give a version of the Moser-Trudinger inequality without boundary condition for Orlicz-Sobolev spaces embedded into exponential and multiple exponential spaces. We also derive the Concentration-Compactness Alternative for this inequality. As an application of our Concentration-Compactness Alternative we prove that a functional with the sub-critical growth attains its maximum.
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