The concept of mapped coercivity for nonlinear operators in Banach spaces

IF 1.7 2区 数学 Q1 MATHEMATICS
Roland Becker , Malte Braack
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引用次数: 0

Abstract

We provide a concise proof of existence of the solutions to nonlinear operator equations in separable Banach spaces, without assuming the operator to be monotone. Instead, our main hypotheses consist of a continuity assumption and a mapped coercivity property, which is a generalization of the usual coercivity property for nonlinear operators. In the case of linear operators, we recover the traditional inf-sup condition. To illustrate the applicability of this general concept, we apply it to semi-linear elliptic problems and the Navier-Stokes equations.
Banach空间中非线性算子的映射矫顽力概念
在不假设算子是单调的前提下,给出了可分离Banach空间中非线性算子方程解的存在性的简明证明。相反,我们的主要假设由连续性假设和映射的矫顽力性质组成,这是非线性算子通常的矫顽力性质的推广。对于线性算子,我们恢复了传统的自适应条件。为了说明这个一般概念的适用性,我们将它应用于半线性椭圆问题和Navier-Stokes方程。
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来源期刊
CiteScore
3.20
自引率
5.90%
发文量
271
审稿时长
7.5 months
期刊介绍: The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis
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