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Results tagged with ap.analysis-of-pdes
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user 123448
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
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Deriving the general interior elliptic estimate from the compactly supported case
This is an exercise (10.3.4 in the third edition) from Nicolaescu's Lectures on the Geometry of Manifolds.
Let $L$ be an elliptic differential operator of order $k$ and $1 < p < \infty$. The book prov …
- 1,141
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Sobolev interpolation inequality for relatively compact subdomains
I was looking at Nicolaescu's Lectures on the Geometry of Manifolds (3rd edition). In Theorem 10.2.29 he presents (without proof) the following inequality:
For $m \geq 1, p \geq 1, 0 < r \leq R$ there …
- 1,141
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Friedrichs mollifiers and Sobolev spaces
$\renewcommand{\epsilon}{\varepsilon}$The following is from John Roe's book Elliptic operators, topology and asymptotic methods. $S$ is a vector bundle on a compact manifold $M$, but I think for my qu …
- 1,942
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If subharmonic functions converge weakly to a subharmonic limit, why do their smoothings con...
Let $u_k$ be a sequence of subharmonic functions on an open set $X$ and $\psi_\delta$ a family of standard mollifiers with compact support. Hörmander claims in The Analysis of Linear Partial Different …
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