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Is $H_0^1([a,b]) \subset C([a,b],\mathbb{R})$?

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#analysis #functional-analysis #sobolev-spaces
100
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$H^1$ norm estimation of an affine function

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#inequality #sobolev-spaces
2.6k
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Surjectivity of the trace operator in Sobolev spaces

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#functional-analysis #partial-differential-equations #sobolev-spaces #trace
200
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$k\in (0,1)$, is $W^{k,p}(\Omega)$ the closure of $C^{0,k}(\overline{\Omega})$ with the $L^p$ norm

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#sobolev-spaces
200
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What is $H^1([0,1]) \otimes H^1([0,1])$?

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#functional-analysis #hilbert-spaces #sobolev-spaces #tensor-products
2.6k
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How exactly does the constant $C$ in the Sobolev inequality depend on the domain?

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#partial-differential-equations #sobolev-spaces
10.1k
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Sobolev space - norm $H^1$ and $H^1_0$

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#functional-analysis #sobolev-spaces #normed-spaces
329
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Nonlinear parabolic PDEs, what methods/techniques for existence?

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#reference-request #partial-differential-equations #sobolev-spaces
38
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Does $f(u)\in H^1$ imply that also the "inner average" $f(u_h)\in H^1$?

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#sobolev-spaces #lebesgue-integral
158
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Defining $W^{k,p}(M)$ for non-integers $k$ and $p$ and manifold $M$

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#functional-analysis #riemannian-geometry #sobolev-spaces
404
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Is the inclusion map in the Sobolev embedding theorem a surjective map?

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#real-analysis #functional-analysis #operator-theory #sobolev-spaces
529
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Definition of weak solutions from geometrical point of view

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#analysis #differential-geometry #partial-differential-equations #intuition #sobolev-spaces
2.9k
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To which Sobolev local space Dirac delta function belongs to?

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#sobolev-spaces
691
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General formula needed for this product rule expression (differential operator)

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#calculus #sobolev-spaces
95
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A $C^1$ function and uniform continuity (Bochner type spaces)

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#functional-analysis #sobolev-spaces

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