Dual characterization of fractional capacity via solution of fractional <i>p</i>‐Laplace equation
Shaoguang Shi, Lei Zhang
Abstract
Abstract In terms of weak solutions of the fractional p ‐Laplace equation with measure data, this paper offers a dual characterization for the fractional Sobolev capacity on bounded domain. In addition, two further results are given: one is an equivalent estimate for the fractional Sobolev capacity; the other is the removability of sets of zero capacity and its relation to solutions of the fractional p ‐Laplace equation.
Topics & Concepts
MathematicsLaplace transformSobolev spaceFractional calculusBounded functionMathematical analysisCharacterization (materials science)Dual (grammatical number)Zero (linguistics)LiteratureLinguisticsArtNanotechnologyPhilosophyMaterials scienceNonlinear Partial Differential EquationsDifferential Equations and Boundary ProblemsNumerical methods in inverse problems