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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

4 votes
0 answers
91 views

Are Sobolev isometries in Minkowski space smooth

Let $\Omega\subset\mathbb{R}^d$ be an open regular domain and let $f\in W^{1,\infty}(\Omega;\mathbb{R}^d)$ satisfy that $df\in\operatorname{SO}(d)$ almost-everywhere. It was proved by Reshetnyak (in a …
Raz Kupferman's user avatar
2 votes
1 answer
171 views

A question about solutions to ordinary differential systems

Consider the second-order ordinary differential system $$ A y'' + i B y' - C y = 0, $$ where $A$ and $C$ are real-valued $d\times d$ SPD matrices satisfying $$ I \le A,C \le 2I, $$ and $B$ is real-val …
Raz Kupferman's user avatar