We consider the nonlinear problem det Du=f in a bounded smooth domain in R^n, with boundary condition u(x) =x where f is in C^{k}(O), kge 1, satisfying a suitable compatibility condition. The positivity of f is a standard assumption in the literature. In a recent joint paper with B.Dacorogna and O.Kneuss (EPFL) we prove the existence of a solution u in C^k(overline{O};R^n) with no assumptions on the sign of f. Here we state this theorem together with some related results and we outline the main features of the problem.
G. Cupini (2010). Sull'equazione det Du = f senza ipotesi di segno. BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR, 1, 1-15 [10.6092/issn.2240-2829/2258].
Sull'equazione det Du = f senza ipotesi di segno
CUPINI, GIOVANNI
2010
Abstract
We consider the nonlinear problem det Du=f in a bounded smooth domain in R^n, with boundary condition u(x) =x where f is in C^{k}(O), kge 1, satisfying a suitable compatibility condition. The positivity of f is a standard assumption in the literature. In a recent joint paper with B.Dacorogna and O.Kneuss (EPFL) we prove the existence of a solution u in C^k(overline{O};R^n) with no assumptions on the sign of f. Here we state this theorem together with some related results and we outline the main features of the problem.| File | Dimensione | Formato | |
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