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Zeitschrift für Analysis und ihre Anwendungen

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Volume 28, Issue 1, 2009, pp. 47–56
DOI: 10.4171/ZAA/1371

Published online: 2009-03-31

Existence of Solutions for some Quasiaffine PDEs

Flavia Giannetti[1] and Giovanni Pisante[2]

(1) Università degli Studi di Napoli Federico II, Italy
(2) Università degli Studi Federico II, Caserta, Italy

We prove the existence of solutions of problems of the type \begin{equation*} \left\{ \begin{aligned} \Phi(Du(x)) &= f(x) &\quad &\text{\rm in } \, \Omega\\ u(x) &=\xi_0 x &\quad &\text{\rm on } \, \partial \Omega \end{aligned} \right. \end{equation*} with $\Phi:\mathbb{R}^{n\times n} \to \mathbb{R}$ quasiaffine function and $\xi_0\in \mathbb{R}^{n\times n}$ fixed.

Keywords: Quasiaffine functions, change of variables, multiplication algebra

Giannetti Flavia, Pisante Giovanni: Existence of Solutions for some Quasiaffine PDEs. Z. Anal. Anwend. 28 (2009), 47-56. doi: 10.4171/ZAA/1371