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Results tagged with sobolev-spaces
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user 74842
A Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself and its derivatives up to a given order.
2
votes
Operator on a Sobolev space
I can't comment yet so let me post as answer. Forget about the coefficients and just take $L=-\Delta$, the Dirichlet Laplacian. Then you are asking why $-\Delta u \in H^{-1}(\Omega)$ when $u \in H^1_0 …
- 171
2
votes
0
answers
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About norm on $H^{\frac 12}(M \times \{0,1\})$
Let $X=M \times \{0,1\}$ with $M$ a smooth compact manifold without boundary.
Define the fractional Sobolev space $H^{\frac 12}(X) = (L^2(X), H^1(X))_{\frac 12}$, as the real interpolation space mid …
- 171