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Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

16 votes
1 answer
761 views

The determinant as a differential operator

According to Gårding, the determinant is a hyperbolic polynomial over the space $\mathbf{Sym}_n$ of real symmetric $n\times n$ matrices. More precisely, it is hyperbolic in the direction of the identi …
Denis Serre's user avatar
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2 votes
0 answers
58 views

Convex solutions of linear hyperbolic PDEs in a planar domain

Consider a linear homogeneous 2nd-order PDE in a convex planar domain $\Omega$ : $$a(x,y)\frac{\partial^2u}{\partial x^2}+2b(x,y)\frac{\partial^2u}{\partial x\partial y}+c(x,y)\frac{\partial^2u}{\part …
Denis Serre's user avatar
  • 52.3k
6 votes
1 answer
619 views

A curious determinant of quadratic forms

In a work about the Wave Equation, I encountered the following symmetric matrix of size $1+n$, whose entries are quadratic forms. The arguments are a scalar $a$ and a vector $X\in k^n$. $$S(a,X)=\beg …
Denis Serre's user avatar
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