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  • Theory
    • Linear Programming
      • The Simplex Algorithm
      • Linear Programming
      • Simplex Pivot Element
      • The 2-Phase Method
      • Duality
      • The online Simplex method
    • Numerical Methods
      • Differential Equations
      • Runge-Kutta Methods
      • Fehlberg Methods
      • Runge-Kutta On line
    • Calculus
      • Derivates
      • Chain Rule
    • Complex analysis
      • The Complex plane
      • Complex variable functions
      • The complex derivate
      • Complex integration
      • Cauchy's integral formula
    • Special Relativity
      • Maxwell's Equations
      • Lorentz
      • Minkowski
      • E=mc2
    • Fourier Analysis
      • Fourier Series
      • Hilbert Spaces
      • Fourier Series Convergence
      • Discontinuities Behavour
      • The Online Fourier Series
    • Non Linear Programming
      • Linear programing Basics
      • Differentiable Functions
      • Convex Functions
      • On line optimizations
      • Lagrange Multipliers
    • Linear Algebra
      • Eigenvalues
      • Matrix Diagonalizations
      • Jordan canonical form
      • Online Systems
    • Differential Geometry
      • Manifolds
      • Tensorial Algebra
      • Geodesics
      • Lagrangian method
  • Apps. Directory
    • 3D-Functions Plotter
    • Runge Kutta Methods
    • The Simplex Algorithm
    • Eigenvalues Calculator
    • 2D-Functions Plotter
    • Functions Analyzer
    • Fourier Series
    • Prime numbers calculator
    • MathsTools Applet
    • Latex Editor
  • Maths Mobile
    • Android Mathstools
      • 3D-Functions Plotter Android
      • Simplex Android Calculator
      • Runge-Kutta Methods
      • Android Integrator
      • Matrix Studio
  • Examples
    • Linear Programming
      • The 2-Phase Method
      • Simplex method example
      • Finite Solution Example
      • Unbounded Solution Sample
      • Infinite Solutions Sample
      • Uncompatible Constraints
    • Numerical Analysis
      • The Euler's method
      • Three eighths rule in Matlab
      • Dormand/Prince 4 and 5
      • Modelling the Brusselator
    • Linear Algebra
      • Jordan Cannonical form 3x3
      • Jordan 3x3(2)
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  • Dictionary
    • Definitions
Sobolev Spaces
The Soblev spaces are space of functions wich derivate up to order k belongs to Lp, formally

Wk, p = {f∈Lp | Dα f ∈Lp, |∈|≤k}

Sobolev espaces are subespaces of Lp, in particular.

Wk, p ⊂ Lp

from this viewpoint

Lp = W0,p

Also, there is a definition in the Fourier Coefficents framework, if f^n is the n-th Fourier coefficient, then



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