Fractional Orlicz-Sobolev embeddings
Angela Alberico, Andrea Cianchi, Luboš Pick, Lenka Slavíková
Abstract
The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz–Sobolev spaces in Rn. An improved embedding with an Orlicz–Lorentz target space, which is optimal in the broader class of all rearrangement-invariant spaces, is also established. Both spaces of order s∈(0,1), and higher-order spaces are considered. Related Hardy type inequalities are proposed as well.
Topics & Concepts
MathematicsPure mathematicsSobolev spaceBirnbaum–Orlicz spaceInvariant (physics)Lorentz transformationEmbeddingLorentz spaceOrder (exchange)Interpolation spaceType (biology)Space (punctuation)Functional analysisMathematical physicsPhysicsGeneComputer sciencePhilosophyEconomicsLinguisticsChemistryBiochemistryArtificial intelligenceBiologyEcologyClassical mechanicsFinanceNonlinear Partial Differential EquationsAdvanced Harmonic Analysis ResearchNumerical methods in engineering