List questions from regularity-theory-of-pdes

Published on 21 Nov 2020 - 15:35

77

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Requiring regularity of solution up to boundary to assure uniqueness for $\Delta u=0$

Published on 30 Nov 2020 - 14:08

388

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Distributional and weak solutions

Published on 10 Dec 2020 - 3:36

86

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Differential analog to the Lebesgue spaces $\mathcal{L}^p$

Published on 25 Mar 2026 - 19:58

91

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Norm in $C^{1}([0,T];H^{s}(\mathbb R^d))$

Published on 19 Dec 2020 - 20:56

36

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Reference request for mixed Sobolev / Lebesgue space

Published on 07 Jan 2021 - 22:25

54

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Finite Element Method and implementation

Published on 24 Feb 2026 - 0:45

158

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On the regularity of Poisson's equation with Robin boundary condition

Published on 13 Jan 2021 - 15:24

207

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Elliptic regularity estimate for Possion with bounded forcing term

Published on 28 Mar 2026 - 8:08

196

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Boundedness of the inverse (Evans) why the chosen subsequence converge in $L^2(U)$

Published on 28 Mar 2026 - 8:09

85

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The regularity for elliptic problems

Published on 26 Mar 2026 - 8:14

12

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Evolutional boundary condition

Published on 26 Feb 2026 - 22:28

76

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Assume $u \in L^\infty ([0,T];H^{s-1})$, $u_t \in L^\infty ([0,T];H^{s-1})$ then can we show that $u \in C([0,T];H^{s-1})$

Published on 25 Mar 2026 - 7:46

158

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What is regularity of solution of Dirichlet problem with Dirac distribution as boundary data?

Published on 21 Feb 2021 - 14:18

85

Views

A solution of the heat equation is more regular where the external force is more regular?

Published on 05 Mar 2021 - 18:20

List Question

If $f$ is continuous and $u \in C^0 \cap H^k$, then is it true that $f(u) \in H^{k}$?

Requiring regularity of solution up to boundary to assure uniqueness for $\Delta u=0$

Distributional and weak solutions

Differential analog to the Lebesgue spaces $\mathcal{L}^p$

Norm in $C^{1}([0,T];H^{s}(\mathbb R^d))$

Reference request for mixed Sobolev / Lebesgue space

Finite Element Method and implementation

On the regularity of Poisson's equation with Robin boundary condition

Elliptic regularity estimate for Possion with bounded forcing term

Boundedness of the inverse (Evans) why the chosen subsequence converge in $L^2(U)$

The regularity for elliptic problems

Evolutional boundary condition

Assume $u \in L^\infty ([0,T];H^{s-1})$, $u_t \in L^\infty ([0,T];H^{s-1})$ then can we show that $u \in C([0,T];H^{s-1})$

What is regularity of solution of Dirichlet problem with Dirac distribution as boundary data?

A solution of the heat equation is more regular where the external force is more regular?

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