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Results tagged with sobolev-spaces
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user 129831
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.
3
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How to rigorously differentiate the convolution of a distribution and a $L^2$ function?
I want to prove the following: (Here, $W^{2,2}$ is a Sobolev space as defined in Evans, chapter 5; $S$ is a Schwartz space; and if $A$ is a distribution and $a$ a function, then $\langle A, a\rangle$ …
- 1,326
2
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answer
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Is the parameter-dependent integral of a Sobolev function continuous?
Let $f\in W^{1,2}_{\text{loc}}(\mathbb R^2)$. Here, $W^{1,2}_{\text{loc}}(\mathbb R^2)$ denotes the usual Sobolev space. More explicitly, $f:\mathbb R^2\to\mathbb R$ is a function such that, for every …
- 1,326
1
vote
Accepted
How to rigorously differentiate the convolution of a distribution and a $L^2$ function?
The last step is formally justified by 15.8, differentiation property of José Sebastião e Silva's "Integrals and orders of growth of distributions." (The paper is currently available here.)
More preci …
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