All Questions
8 questions with no upvoted or accepted answers
3
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588
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Propagation of Singularities
I'm following the book "Elementary Introduction To The Theory Of Pseudodifferential Operators" by X. S. Raymond and the Joshi Lectures Notes - https://arxiv.org/pdf/math/9906155.pdf - to prove the ...
- 509
2
votes
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67
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Asking a reference for a fact about nonlocal operators
Let assume that $u$ is smooth enough and $ -\Delta (u \phi) \in L^1(\Omega)$ for any $\phi \in C_c^{\infty}(\Omega)$. Then it easily follows that $ -\Delta u \in L^1_{\mathrm{loc}}(\Omega)$ by ...
- 371
2
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315
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Support of a microlocal defect measure
I'm trying to complete the proof of the Theorem 6.1 in the notes https://www.math.u-psud.fr/~nb/articles/coursX.pdf, which ensures, under certain conditions, that the support of the microlocal defect ...
- 509
2
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0
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40
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Production of $H^s$ singularities in the strictly hyperbolic Cauchy problem
This question is a spin-off from Hyperbolic PDEs - Proof that the restriction of a locally $H^s$ solution to a spacelike hypersurface is locally in $H^s$ as I am trying to find a solution without ...
- 503
1
vote
0
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97
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Oscillatory integrals and regularity
Let $U\subset\mathbb{R}^{d}$ be open and $N\in\mathbb{N}$. Furthermore, let $a\in\mathcal{S}^{m}_{\rho,\sigma}(U\times\mathbb{R}^{N})$ be a symbol and $\Phi\in C^{\infty}(U\times (\mathbb{R}^{N}\...
- 1,171
1
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323
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Does Morrey's inequality contextually relate to Rellic-Kondrachov compactness?
I have been reflecting on this question, and want to share my thinking thus far. I'd be grateful for the community's inputs.
We refer to Morrey's inequality, Theorem 4 on pp 266 of Evan's book on PDE, ...
1
vote
0
answers
70
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Normal form of Principal type $\Psi$DO's
Suppose we have a pseudo differential operator of principal type with a complex symbol and such that the poisson bracket of the real and imaginary parts on the characteristic set is non-negative.I ...
- 4,135
0
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244
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Holder continuity relative to Rellic-Kondrachov compactness via the nonlinear Aronsson operator
Connected to the question,
Does Morrey's inequality contextually relate to Rellic-Kondrachov compactness?
An analysis of the well-known nonlinear Aronsson operator gives $C^{(1, \frac{1}{3})}$ ...