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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

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 …
Tom LaGatta's user avatar
  • 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 …
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 $u = 0$ …
Tom LaGatta's user avatar
  • 8,532