List questions from partial-differential-equations

Published on 11 May 2026 - 1:38

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Differential equation which has following solution $y=\frac{1}{1+\exp(ax)}$

Published on 08 Apr 2026 - 23:47

268

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Integral over compact boundary is finite in the context of potential function

Published on 10 Apr 2026 - 7:53

740

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Solving the PDE $u_{tt}+2u_{tx}+u_{xx}=2c$

Published on 14 Apr 2026 - 6:15

98

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Proper domain for Laplacian

Published on 14 Apr 2026 - 0:25

645

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Why is the integral of $\|\nabla f\|^2$ called the energy of $f$?

Published on 11 May 2026 - 1:53

103

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Domain Schrödinger equation

Published on 14 Apr 2026 - 9:11

149

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$1/r^2\int_{\mathbb{S}_r}u-u(x)$ converging to $\Delta u(x)$?a

Published on 15 Apr 2026 - 22:17

1.8k

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Interior $H^2$ regularity - applying "Cauchy's inequality with $\epsilon$"

Published on 13 Apr 2026 - 17:19

495

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Interior $H^2$ regularity - inequalities over regions $U$ and $W \subset U$

Published on 11 May 2026 - 10:09

178

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Finite difference scheme for hyperbolic system

Published on 11 May 2026 - 5:10

767

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Higher interior regularity

Published on 10 Apr 2026 - 8:42

36

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$\|f(x)\|_{L^p(\mathbb R)} \le C_{>0} \|(1+x^2)^{k/2} f(x)\|_{L^\infty(\mathbb R)} $ holds?

Published on 16 Apr 2026 - 5:23

59

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Prove $F(r)=Cr^2\log(r)$ is a fundamental solution for $\Delta^2$ in $\mathbb R^2$

Published on 15 May 2026 - 15:19

735

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On the solution of constant coefficients PDEs (exponential method)

Published on 10 Apr 2026 - 20:50

List Question

estimation of gradient

Differential equation which has following solution $y=\frac{1}{1+\exp(ax)}$

Integral over compact boundary is finite in the context of potential function

Solving the PDE $u_{tt}+2u_{tx}+u_{xx}=2c$

Proper domain for Laplacian

Why is the integral of $\|\nabla f\|^2$ called the energy of $f$?

Domain Schrödinger equation

$1/r^2\int_{\mathbb{S}_r}u-u(x)$ converging to $\Delta u(x)$?a

Interior $H^2$ regularity - applying "Cauchy's inequality with $\epsilon$"

Interior $H^2$ regularity - inequalities over regions $U$ and $W \subset U$

Finite difference scheme for hyperbolic system

Higher interior regularity

$\|f(x)\|_{L^p(\mathbb R)} \le C_{>0} \|(1+x^2)^{k/2} f(x)\|_{L^\infty(\mathbb R)} $ holds?

Prove $F(r)=Cr^2\log(r)$ is a fundamental solution for $\Delta^2$ in $\mathbb R^2$

On the solution of constant coefficients PDEs (exponential method)

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