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Results tagged with sobolev-spaces
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user 138705
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.
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Trace theorem for $L^2([0,1]; H^k(S^2))$
Consider a function $u$ in $L^2([0,1]; H^k(S^2))$ where $k$ is a positive integer.
Where would $u(0)$ live (or $u(r)$ for some fixed $r \in [0,1]$)? Is there a version of the trace theorem saying that …
- 969
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Two definitions of Sobolev spaces and the trace theorem
Let $M=[0,\infty) \times S^2$. We have the regular regular Sobolev space $H^1(M)$.
We also have the space $H^1\bigg([0,\infty); H^1(S^2)\bigg)$. Are those two spaces the same? Does one contain the oth …
- 969
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Weighted Sobolev norm in terms of Spherical harmonics coefficients
Let $M = [1,\infty) \times S^2$.
Consider the weighted Sobolev space $H^k_{\delta}(M)$ with the Sobolev norm:
$$\lVert u \rVert_{k,\delta}^2 := \sum_{n=0}^k \int_M |D^nu \,r^{n-\delta}|^2 r^{-3} dV $$ …
- 969