JournalszaaVol. 28 , No. 1DOI 10.4171/zaa/1371

Existence of Solutions for some Quasiaffine PDEs

  • Flavia Giannetti

    Università degli Studi di Napoli Federico II, Italy
  • Giovanni Pisante

    Università degli Studi Federico II, Caserta, Italy
Existence of Solutions for some Quasiaffine PDEs cover

Abstract

We prove the existence of solutions of problems of the type

{Φ(Du(x))=f(x)in Ωu(x)=ξ0xon Ω\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.

with Φ:Rn×nR\Phi:\mathbb{R}^{n\times n} \to \mathbb{R} quasiaffine function and ξ0Rn×n\xi_0\in \mathbb{R}^{n\times n} fixed.