List questions from elliptic-equations

Published on 03 Mar 2017 - 10:55

41

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Description of strongly elliptic functions

Published on 25 Mar 2026 - 14:39

198

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The bounded solution of $\Delta u=u$ in $\mathbb R^3$ must be zero.

Published on 05 Mar 2017 - 11:17

104

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If $L$ is elliptic, is $\partial_t - L$ hypoelliptic?

Published on 25 Mar 2026 - 14:39

58

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If the eigenfunction $u\in C^2(B_1)\cap C(\overline{B_1})$ of $-\Delta u=u$ vanishes at $B_{1/2}$, then $u$ must be zero?

Published on 14 Mar 2017 - 14:58

490

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Why is the de Rham complex elliptic?

Published on 21 Mar 2017 - 12:09

525

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Harnack's inequality of elliptic PDE

Published on 26 Mar 2026 - 6:28

78

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Maximum of elliptic PDE

Published on 29 Jan 2023 - 18:52

33

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A maximum principle for elliptical operator in $\mathbb{R}^N$

Published on 23 Feb 2026 - 12:02

435

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Analytical solution for 2D Advection-diffusion equation considering Dirichlet/Neumann BC

Published on 04 Feb 2023 - 9:56

75

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Hölder estimates of derivatives of harmonic function?

Published on 07 Feb 2023 - 6:39

27

Views

Inequality for a harmonic equation

Published on 12 Feb 2023 - 19:33

35

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A maximum principle in $\mathbb{R}^N$

Published on 25 Mar 2026 - 14:39

88

Views

Case n=2 in boundedness of subelliptic operator (Gilbarg-Trudinger Theorem 8.15)

Published on 14 Feb 2023 - 19:14

108

Views

Evans: Energy estimates for elliptic PDE. why is the Poincare inequality necessary?

Published on 17 Feb 2023 - 19:57

List Question

R.H.S. of Poisson equation localized $\Rightarrow$ Solution localized

Description of strongly elliptic functions

The bounded solution of $\Delta u=u$ in $\mathbb R^3$ must be zero.

If $L$ is elliptic, is $\partial_t - L$ hypoelliptic?

If the eigenfunction $u\in C^2(B_1)\cap C(\overline{B_1})$ of $-\Delta u=u$ vanishes at $B_{1/2}$, then $u$ must be zero?

Why is the de Rham complex elliptic?

Harnack's inequality of elliptic PDE

Maximum of elliptic PDE

A maximum principle for elliptical operator in $\mathbb{R}^N$

Analytical solution for 2D Advection-diffusion equation considering Dirichlet/Neumann BC

Hölder estimates of derivatives of harmonic function?

Inequality for a harmonic equation

A maximum principle in $\mathbb{R}^N$

Case n=2 in boundedness of subelliptic operator (Gilbarg-Trudinger Theorem 8.15)

Evans: Energy estimates for elliptic PDE. why is the Poincare inequality necessary?

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