The concentration-compactness principles for W <sup> <i>s,p</i> (·,·) </sup> (ℝ <i> <sup>N</sup> </i> ) and application
Ky Ho, Yun-Ho Kim
Abstract
Abstract We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.
Topics & Concepts
Compact spaceSobolev spaceMathematicsCritical exponentExponentConstant (computer programming)Class (philosophy)Mathematical analysisVariable (mathematics)PhysicsCombinatoricsGeometryScalingProgramming languagePhilosophyLinguisticsArtificial intelligenceComputer scienceNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringAdvanced Mathematical Physics Problems