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Results tagged with ap.analysis-of-pdes
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user 109191
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
2
votes
0
answers
76
views
Boundary value spaces
In Uhlenbecks paper Connections with $L^p$ bounds on curvature [p.38, l. 2-4] it is noted that a certain boundary value problem may be solved by using "boundary value spaces". A book of Katrin Wehrhei …
- 381
4
votes
2
answers
857
views
Principal symbol for non-linear differential operators
$\newcommand{\R}{\mathrm{R}} \newcommand{\N}{\mathrm{N}}\newcommand{\DD}{\mathrm{D}}\newcommand{\dd}{\mathrm{d}}$
Prerequisites: Let $\mathrm{T}: C^\infty(\Omega) \rightarrow
C^\infty(\Omega), u(\cdo …
- 381
5
votes
1
answer
298
views
$L^p$-estimates for elliptic pseudodifferential operators
Assume we have an pseudodifferential operator
$P:\mathcal{S}(\mathbb{R}^n) \rightarrow \mathcal{S}(\mathbb{R}^n), Pf(x) = (2\pi)^{-n/2}\int\mathrm{d}\xi\; p(x,\xi)\,\hat{f}(\xi)e^{i\xi x}$
acting on …
- 381
3
votes
2
answers
429
views
Resources on Elliptic Boundary Value Problems on manifolds
My situation:
I am currently trying to understand Uhlenbecks results on the Yang Mills equation. One of the most common notions in this paper is that of an elliptic system or an elliptic boundary valu …
- 381