List questions from partial-differential-equations

Published on 25 Mar 2026 - 12:47

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Potential flow around a torus - Laplace equation in toroidal coordinates

Published on 24 Mar 2026 - 22:11

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Constants in the inequality $\| u\|_{L^p} \le C \| Lu\|_{L^p}$.

Published on 24 Mar 2026 - 23:45

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Clarification on quantum optimal control problem

Published on 25 Mar 2026 - 8:06

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Why does $w=u-h$ satisfy mean value property on any ball inside $B$?

Published on 25 Mar 2026 - 6:02

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Embedding of $S^n$ under harmonic map heat flow

Published on 25 Mar 2026 - 14:04

48

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Why does $\underset {x \in \Omega'}{\mathrm {inf}}\ |u_m (x) - u_n (x)| \le \epsilon$?

Published on 25 Mar 2026 - 7:43

792

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Hyperbolic PDEs and Characteristic Curves

Published on 25 Mar 2026 - 15:42

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Step in the motivation of Lax-Milgram with membrane problem.

Published on 25 Mar 2026 - 23:37

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For $u$ in the Sobolev space $W^{k,p}(U)$, how to know $u$ or $D^\alpha u$ on the boundary of $U$?

Published on 25 Mar 2026 - 8:13

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Let $M$ is compact Riemann surface, if $\omega$ is a 2-form and $\int_{M} \omega =0$ then there exists a smooth function $f$ such that $\omega=d*df$

Published on 04 Apr 2026 - 3:43

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If $u$ is real valued function on $\Omega \subset \Bbb R^n$ then what is meant by $D^{\alpha} u$?

Published on 22 Apr 2018 - 17:04

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If $u$ is harmonic then $Du$ is harmonic.

Published on 25 Mar 2026 - 6:00

46

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is it possible to have $u(1,t) = 10$ and $u(x,0) = x^2$ for $x \in [0,1]$? (heat equation)

Published on 25 Mar 2026 - 3:03

216

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Integral of second moment

Published on 04 Apr 2026 - 5:28

List Question

How can Dirichlet eigenvalues be defined for closed sets?

Potential flow around a torus - Laplace equation in toroidal coordinates

Constants in the inequality $\| u\|_{L^p} \le C \| Lu\|_{L^p}$.

Clarification on quantum optimal control problem

Why does $w=u-h$ satisfy mean value property on any ball inside $B$?

Embedding of $S^n$ under harmonic map heat flow

Why does $\underset {x \in \Omega'}{\mathrm {inf}}\ |u_m (x) - u_n (x)| \le \epsilon$?

Hyperbolic PDEs and Characteristic Curves

Step in the motivation of Lax-Milgram with membrane problem.

For $u$ in the Sobolev space $W^{k,p}(U)$, how to know $u$ or $D^\alpha u$ on the boundary of $U$?

Let $M$ is compact Riemann surface, if $\omega$ is a 2-form and $\int_{M} \omega =0$ then there exists a smooth function $f$ such that $\omega=d*df$

If $u$ is real valued function on $\Omega \subset \Bbb R^n$ then what is meant by $D^{\alpha} u$?

If $u$ is harmonic then $Du$ is harmonic.

is it possible to have $u(1,t) = 10$ and $u(x,0) = x^2$ for $x \in [0,1]$? (heat equation)

Integral of second moment

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