We consider the nonlinear problemdet?u (x) = f (x) x ? u (x) = x x ? ?where k ? 1 is an integer, is a bounded smooth domain in Rn and f ? Ck ???? satisfiesZf (x) dx = meas.The positivity of f is a standard assumption in the literature. In a recent joint paper withB.Dacorogna and O.Kneuss (EPFL) we prove the existence of a solution u ? Ck ????;Rn with no assumptions on the sign of f. Here we state this theorem together with somerelated results and we outline the main features of the problem.
@article{2258,
title = {Sull'equazione det Du = f senza ipotesi di segno},
journal = {Bruno Pini Mathematical Analysis Seminar},
year = {2010},
doi = {10.6092/issn.2240-2829/2258},
language = {IT},
url = {http://dml.mathdoc.fr/item/2258}
}
Cupini, Giovanni. Sull’equazione det Du = f senza ipotesi di segno. Bruno Pini Mathematical Analysis Seminar, (2010), . doi : 10.6092/issn.2240-2829/2258. http://gdmltest.u-ga.fr/item/2258/