Sharp Sobolev and Adams–Trudinger–Moser embeddings on weighted Sobolev spaces and their applications
João Marcos do Ó, Guozhen Lu, Raoní Ponciano
Abstract
Abstract We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential class with a sharp constant. As applications, we prove that the associated elliptic equations with nonlinearities in both forms of polynomial and exponential growths admit nontrivial solutions.
Topics & Concepts
Sobolev spaceMathematicsSobolev inequalitySobolev spaces for planar domainsEmbeddingClass (philosophy)Exponential functionPure mathematicsConstant (computer programming)PolynomialBoundary (topology)Type (biology)Mathematical analysisInterpolation spaceFunctional analysisChemistryEcologyBiochemistryGeneArtificial intelligenceBiologyComputer scienceProgramming languageNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Boundary Problems