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Is $H^1(\Omega) \cap C_c(\Omega)$ dense in $C_c(\Omega)$?

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#functional-analysis #sobolev-spaces
30
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equality wrt $W_2^1$ norm

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#partial-differential-equations #normed-spaces #sobolev-spaces
42
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example - functional in $H^{-1}(\Omega)$

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#partial-differential-equations #sobolev-spaces #distribution-theory
99
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Are continuous weakly $p$-harmonic maps smooth?

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#analysis #reference-request #sobolev-spaces #harmonic-functions #regularity-theory-of-pdes
197
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Sobolev Compact Embedding in Brezis' books

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#real-analysis #functional-analysis #compactness #sobolev-spaces
74
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$f \in H^1_0(\Omega)$ , $g \in W^{1,\infty}_{loc} \Rightarrow fg \in H_0^1$?

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#sobolev-spaces
455
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Characterization of weak convergence in $W^{1, p}(\Omega)$

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#functional-analysis #sobolev-spaces #lp-spaces #weak-convergence
381
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What is the meaning of this notation $W^{1, \infty}(\Omega, \mathbb R^m)$?

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#partial-differential-equations #notation #sobolev-spaces
26
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Is $b(\min(u^+,1),\min(u^+,1)) \leq b(u,u)$ equivalent to $b(u^+,u^-) \leq 0$?

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#functional-analysis #sobolev-spaces
126
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Is $H^s(\Omega) \cap C_0(\bar\Omega) \subset H^s(\Omega)$ dense?

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#reference-request #sobolev-spaces
163
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On a Sobolev embedding: every $u\in W^{1,p}(I)$ is Bounded

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#sobolev-spaces
407
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Does $F(x)=\int_0^xf(y)dy$ have a weak derivative?

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#integration #sobolev-spaces #distribution-theory #weak-derivatives
74
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Problem concerning $H^{-1}$ space

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#sobolev-spaces #dual-spaces
371
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Multiplication by a compactly supported function is a compact operator

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#analysis #manifolds #sobolev-spaces
1.1k
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Importance of Sobolev Spaces within PDE besides for weak solutions

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#partial-differential-equations #sobolev-spaces

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