Publication

Existence Of Solutions For Jacobian And Hessian Equations Under Smallness Assumptions

Bernard Dacorogna, Sébastien Basterrechea
2014
Journal Articles

Abstract

We discuss three types of problems. The first one involves Jacobian equations and the two others involve Hessian equations. We proceed by fixed point, obtaining the results under a smallness assumption.

Official source

https://infoscience.epfl.ch/entities/publication/9396f239-f450-4b4c-b0fd-3020b66f5608

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Bernard Dacorogna, Sébastien Basterrechea
2014
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/9396f239-f450-4b4c-b0fd-3020b66f5608

About this result

Related concepts (18)

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

Fixed-point iteration

In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.

Fixed-point theorem

In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. The Banach fixed-point theorem (1922) gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point.

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