在方程det Du = f上，没有符号假设

IF 0.2 Q4 MATHEMATICS

Bruno Pini Mathematical Analysis Seminar Pub Date : 2010-12-30 DOI:10.6092/ISSN.2240-2829/2258

G. Cupini

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引用次数: 0

摘要

我们考虑非线性问题det?U (x) = f (x) x ?U (x) = x ?？ k在哪里?1是一个整数，是Rn和f中的有界光滑定义域吗?Ck ? ?满足zf (x) dx =均值。f的正性是文献中的一个标准假设。在最近与B.Dacorogna和O.Kneuss (EPFL)的一篇联合论文中，我们证明了u ?Ck ? ?在这里，我们陈述了这个定理以及一些相关的结果，并概述了这个问题的主要特征。

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Sull’equazione det Du = f senza ipotesi di segno

We consider the nonlinear problem det?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 ???? satisfies Z f (x) dx = meas . 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 ? Ck ???? ;Rn 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.

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来源期刊

Bruno Pini Mathematical Analysis Seminar MATHEMATICS-

CiteScore

0.30

自引率

0.00%

发文量

审稿时长

15 weeks