Improved Adams-type inequalities and their extremals in dimension 2m
Azahara DelaTorre, Gabriele Mancini
Abstract
In this paper, we prove the existence of an extremal function for the Adams–Moser–Trudinger inequality on the Sobolev space [Formula: see text], where [Formula: see text] is any bounded, smooth, open subset of [Formula: see text], [Formula: see text]. Moreover, we extend this result to improved versions of Adams’ inequality of Adimurthi-Druet type. Our strategy is based on blow-up analysis for sequences of subcritical extremals and introduces several new techniques and constructions. The most important one is a new procedure for obtaining capacity-type estimates on annular regions.
Topics & Concepts
MathematicsDimension (graph theory)Sobolev inequalityFunction (biology)InequalitySobolev spaceSpace (punctuation)Pure mathematicsLinear inequalityFunction spaceApplied mathematicsMathematical analysisLog sum inequalityCharacterization (materials science)Real-valued functionDiscrete mathematicsNonlinear Partial Differential EquationsAnalytic and geometric function theoryMathematical functions and polynomials