Bulletin of the American Mathematical Society · 1973 · 43 citations · 2 references
EngineeringComputational EngineeringTopologyBoundary ConditionsHarmonic AnalysisPartial Differential EquationsSpline CurvesVariational FormulationWeak FormulationConvex Variational ProblemsNonlinear Variational ProblemsSobolev SpacesSplinesVariational Methods In Partial Differential EquationsVariational ProblemsWeak Form Of Partial Differential Equations
The Sobolev space W^\a9 b] is comprised of all functions ƒ defined on [a9b] where/ (w-1) is absolutely continuous and the maximum norm of its nth derivative || ƒ ||00 is finite. For ease of exposition, henceforth let [a, b] = [0,1]. Let x1 < x2 < . . . < xn+r be n + r prescribed points in [0,1] and {af}=i given real numbers. Consider the subset *ƒ[#, a] of W£ consisting of all feW£ interpolating the data {af} at {x,}; i.e., feWTM satisfies
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