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Results tagged with ap.analysis-of-pdes
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user 238
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
11
votes
1
answer
988
views
Prescribing Gaussian curvature
Let $K(r)$ be the piecewise function
I want to solve the PDE $$\Delta u + K(|x|) e^{2u} = 0$$ for radially symmetric $u$ with boundary condition $u = 0$ …
- 8,532
4
votes
Open problems in PDEs, dynamical systems, mathematical physics
Percolation is a major outstanding research area in both theoretical and applied probability. I recommend reading the recent survey Percolation Since St. Flour by Geoffrey Grimmett and Harry Kesten (J …
2
votes
Is the derivative of a Lipschitz function better than L^\infty
Every Lipschitz function is absolutely continuous. Consequently, its derivative exists and is uniformly bounded almost everywhere. The Lipschitz constant is just the $L^\infty$ norm of the derivativ …
- 8,532