Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications
Abstract
We study boundedness, optimality and attainability of Trudinger-Moser type maximization problems in the radial and the subcritical homogeneous Sobolev spaces W1,p0, rad(BRN)\,(p<N). Our results give a revision of an error in [Theorem C]HL. Also, our inequality converges to the original Trudinger-Moser inequality as p N including optimal exponent and concentration limit. Finally, we consider an application of our inequality to elliptic problems with exponential nonlinearity.
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