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On local non-zero constraints in PDE with analytic coefficients

Abstract:

We consider the Helmholtz equation with real analytic coefficients on a bounded domain $\Omega\subset\mathbb{R}^{d}$. We take $d+1$ prescribed boundary conditions $f^{i}$ and frequencies $\omega$ in a fixed interval $[a,b]$. We consider a constraint on the solutions $u_{\omega}^{i}$ of the form $\zeta(u_{\omega}^{1},\ldots,u_{\omega}^{d+1},\nabla u_{\omega}^{1},\ldots,\nabla u_{\omega}^{d+1})\neq0$, where $\zeta$ is analytic, which is satisfied in $\Omega$ when $\omega=0$. We show that for an...

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publication date:
2015-01-07
Keywords:
Pubs id:
pubs:503519
UUID:
uuid:0ccbe46d-e17e-4855-b860-945400113f52
Local pid:
pubs:503519
Source identifiers:
503519
Deposit date:
2015-05-25

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