List questions from regularity-theory-of-pdes

Published on 26 Mar 2026 - 19:24

25

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Boundedness of composition of an inverse of an elliptic differential operator with a differential operator

Published on 06 Nov 2023 - 19:41

33

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Solution of PDE on Lipschitz domain which is in $\{ u \in H^1_0 : \Delta u \in L^2\}$ but not in $H^2$

Published on 26 Mar 2026 - 19:20

17

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references for 2nd order elliptic boundary value problems

Published on 25 Mar 2026 - 17:51

72

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If $u \in L^p$ and $\Delta u \in L^p$ as well, do we necessarily have $u \in W^{2,p}$ for $1<p<\infty$?

Published on 22 Nov 2023 - 1:57

39

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Tricky confusion with the definition of a weak solution for the linear parabolic equations

Published on 26 Mar 2026 - 3:12

27

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$-\Delta u =f $ for $f\in L^p(\Omega)$ implies $\nabla u \in L^p(\Omega)$

Published on 26 Mar 2026 - 21:14

38

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The regularity of two functions and their convolution

Published on 02 Dec 2023 - 23:07

67

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Obtain $L^\infty$ estimate of Poisson Equation only using eigenfunction expansion

Published on 26 Mar 2026 - 16:23

27

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If $\partial_t u_n -\Delta u_n = f_n$ , $\partial_t u -\Delta u =f$ and $f_n \to f$ in $L_t^p L_x^q$, do we have $u_n \to u$ in $W^{1,p}_t L^q_x$?

Published on 26 Mar 2026 - 6:42

37

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Regularity of "spatial Sobolev functions"

Published on 07 Dec 2023 - 14:31

13

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Show $v(x,t) \in L^2([0,T];H^2(\mathbb{R}))$ when $v(x,t)$ is a transformation of a $L^2([0,T];H^2(\mathbb{R}))$ function

Published on 26 Mar 2026 - 8:00

52

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Energy method for linear advection

Published on 12 Dec 2023 - 10:25

62

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If $u(.,t) \in H^2(\mathbb{R})$, then $u (.,t) \in C^1(\mathbb{R})$?

Published on 14 Dec 2023 - 21:28

22

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Energy estimate Neumann Problem with paramter

Published on 19 Dec 2023 - 14:36

List Question

Elliptic regularity in a weird domain

Boundedness of composition of an inverse of an elliptic differential operator with a differential operator

Solution of PDE on Lipschitz domain which is in $\{ u \in H^1_0 : \Delta u \in L^2\}$ but not in $H^2$

references for 2nd order elliptic boundary value problems

If $u \in L^p$ and $\Delta u \in L^p$ as well, do we necessarily have $u \in W^{2,p}$ for $1<p<\infty$?

Tricky confusion with the definition of a weak solution for the linear parabolic equations

$-\Delta u =f $ for $f\in L^p(\Omega)$ implies $\nabla u \in L^p(\Omega)$

The regularity of two functions and their convolution

Obtain $L^\infty$ estimate of Poisson Equation only using eigenfunction expansion

If $\partial_t u_n -\Delta u_n = f_n$ , $\partial_t u -\Delta u =f$ and $f_n \to f$ in $L_t^p L_x^q$, do we have $u_n \to u$ in $W^{1,p}_t L^q_x$?

Regularity of "spatial Sobolev functions"

Show $v(x,t) \in L^2([0,T];H^2(\mathbb{R}))$ when $v(x,t)$ is a transformation of a $L^2([0,T];H^2(\mathbb{R}))$ function

Energy method for linear advection

If $u(.,t) \in H^2(\mathbb{R})$, then $u (.,t) \in C^1(\mathbb{R})$?

Energy estimate Neumann Problem with paramter

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