List questions from sobolev-spaces

Published on 05 May 2026 - 19:30

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$\mbox{Cap}_p$-measurability

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186

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If $u\in W^{1,p}(\Omega )$ is s.t. $\nabla u=0$ then $u$ is constant a.e.

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Weak formulation of Robin boundary condition problem

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676

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Variational Formulation - inhomogeneous Neumann boundary

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50

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Why the Sobolev space $W^{1,2}(M,N)$ weak-sequencially closed in $W^{1,2}(\mathbb R^K)$?

Published on 07 May 2026 - 11:31

302

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Sobolev space $H^s(Q)$ is Hilbert

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Duhamel's principle for heat equation.

Published on 10 May 2026 - 9:25

144

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How to define discrete Sobolev dual norm so that it can be computed?

Published on 29 Apr 2026 - 12:16

242

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Weakly sequentially continuous maps

Published on 07 May 2026 - 11:33

882

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Inclusion map between Sobolev space

Published on 29 Apr 2026 - 12:16

254

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Constant for Sobolev inequality on annulus

Published on 29 Apr 2026 - 12:16

594

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Example 3 - Section 5.5.2 - Partial Differential Equations by Evans

Published on 29 Apr 2026 - 12:16

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$-\nabla \cdot (A\nabla u)=f$ has a weak solution in $H^1$ $\iff$ $\int_\Omega f+\int_{\partial \Omega }g=0$.

Published on 07 May 2026 - 7:35

266

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$H^{\frac12}$ norm and preimage via the trace operator

Published on 05 May 2026 - 10:15

List Question

On sufficient condition for pre-compactness "in measure"(i.e. in Young measure space)

$\mbox{Cap}_p$-measurability

If $u\in W^{1,p}(\Omega )$ is s.t. $\nabla u=0$ then $u$ is constant a.e.

Weak formulation of Robin boundary condition problem

Variational Formulation - inhomogeneous Neumann boundary

Why the Sobolev space $W^{1,2}(M,N)$ weak-sequencially closed in $W^{1,2}(\mathbb R^K)$?

Sobolev space $H^s(Q)$ is Hilbert

Duhamel's principle for heat equation.

How to define discrete Sobolev dual norm so that it can be computed?

Weakly sequentially continuous maps

Inclusion map between Sobolev space

Constant for Sobolev inequality on annulus

Example 3 - Section 5.5.2 - Partial Differential Equations by Evans

$-\nabla \cdot (A\nabla u)=f$ has a weak solution in $H^1$ $\iff$ $\int_\Omega f+\int_{\partial \Omega }g=0$.

$H^{\frac12}$ norm and preimage via the trace operator

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