List questions from elliptic-operators

Published on 14 Apr 2026 - 16:52

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What is an example of harmonic form on a compact manifold?

Published on 10 May 2026 - 16:56

30

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Does there exist any solution for this inequality?

Published on 10 May 2026 - 16:30

586

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First eigenvalue of laplacian on a cylinder

Published on 12 Apr 2026 - 1:01

113

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Non-trivial solution to certain elliptic PDE implies exponential growth.

Published on 11 Apr 2026 - 2:12

834

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Theorem $2$ (Variational principle for the principal eigenvalue)

Published on 12 Apr 2026 - 17:37

260

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Is the Nelson-Laplacian $\sum_{i=1}^{n}X_{i}^{2}$ on a Lie group $G$ an elliptic differential operator?

Published on 14 Apr 2026 - 1:29

67

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Existence of solution to this PDE

Published on 13 Apr 2026 - 18:10

69

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Solving Equations of operators with the delta function (Example)

Published on 11 Apr 2026 - 16:35

412

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Reference Request: First Eigenvalue of Elliptic Operator

Published on 12 Apr 2026 - 11:58

291

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Elliptic Regularity for $C^k$-norms

Published on 16 Apr 2026 - 20:51

96

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If $u_n$ is bounded and pointwise convergent, then $u_n$ convges in $W_{2,p}$.

Published on 17 Apr 2026 - 6:01

1.8k

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Why are Dirichlet eigenfunctions real-analytic?

Published on 14 Apr 2026 - 3:16

184

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When does weakly elliptic $\Rightarrow$ strongly elliptic?

Published on 12 Apr 2026 - 14:25

861

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Why is this bilinear form elliptic on $H^1_0$?

Published on 16 Apr 2026 - 6:34

List Question

Existence of convex defining functions for convex domains

What is an example of harmonic form on a compact manifold?

Does there exist any solution for this inequality?

First eigenvalue of laplacian on a cylinder

Non-trivial solution to certain elliptic PDE implies exponential growth.

Theorem $2$ (Variational principle for the principal eigenvalue)

Is the Nelson-Laplacian $\sum_{i=1}^{n}X_{i}^{2}$ on a Lie group $G$ an elliptic differential operator?

Existence of solution to this PDE

Solving Equations of operators with the delta function (Example)

Reference Request: First Eigenvalue of Elliptic Operator

Elliptic Regularity for $C^k$-norms

If $u_n$ is bounded and pointwise convergent, then $u_n$ convges in $W_{2,p}$.

Why are Dirichlet eigenfunctions real-analytic?

When does weakly elliptic $\Rightarrow$ strongly elliptic?

Why is this bilinear form elliptic on $H^1_0$?

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