Approximation in Sobolev spaces by piecewise affine interpolation

作者：Van Schaftingen Jean^*

来源：Journal of Mathematical Analysis and Applications, 2014, 420(1): 40-47.

DOI：10.1016/j.jmaa.2014.05.036

• Sobolev space
• Piecewise affine function
• Linear interpolation
• Lagrange interpolation
• Approximation
• Density

Functions in a Sobolev space are approximated directly by piecewise affine interpolation in the norm of the space. The proof is based on estimates for interpolations and does not rely on the density of smooth functions.

• 出版日期2014-12-1