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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

1 vote
1 answer
114 views

Friedrich's second inequality for functions with zero average

Friedrich's second inequality (or Maxwell Estimates or Gaffney’s inequality in the literature) is referred as follows: for all $\mathbf{u} \in H^1(\Omega)^2$ satisfying either $\mathbf{n} \cdot \mathb …
Ryan Li's user avatar
  • 31
2 votes
0 answers
62 views

Localized estimate for divergence free vector field

Suppose $\Omega \subset \mathbb{R}^3$ is a simply connected Lipchitz domain. For a divergence free field $w\in [L^2(\Omega)]^d$, it is well known that there exists a vector field $v\in [W^{1,2}(\Omega …
Ryan Li's user avatar
  • 31
0 votes

Finite element method inverse estimate

You may take a look at Theorem 3.2.6 p140 in the book Philippe G. Ciarlet, The Finite Element Method for Elliptic Problems.
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