On the exterior Dirichlet problem for Hessian type fully nonlinear elliptic equations

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Xiaoliang Li, Cong Wang
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引用次数: 1

Abstract

. We treat the exterior Dirichlet problem for a class of fully nonlinear elliptic equations of the form f ( λ ( D 2 u )) = g ( x ) , with prescribed asymptotic behavior at infinity. The equations of this type had been studied extensively by Caffarelli–Nirenberg–Spruck [8], Trudinger [35] and many others, and there had been significant discussions on the solv- ability of the classical Dirichlet problem via the continuity method, under the assumption that f is a concave function. In this paper, based on the Perron’s method, we establish an exterior existence and uniqueness result for viscosity solutions of the equations, by assuming f to satisfy certain structure condi- tions as in [8, 35] but without requiring the concavity of f . The equations in our setting may embrace the well-known Monge–Amp`ere equations, Hessian equations and Hessian quotient equations as special cases.
Hessian型全非线性椭圆方程的外狄利克雷问题
。我们处理了一类形式为f (λ (d2 u)) = g (x)的完全非线性椭圆方程的外部Dirichlet问题,该方程在无穷远处具有规定的渐近行为。Caffarelli-Nirenberg-Spruck [8], Trudinger[8]等人对这类方程进行了广泛的研究,并在假设f为凹函数的情况下,对经典Dirichlet问题用连续性方法的可解性进行了有意义的讨论。本文基于Perron方法,假设f满足[8,35]中的某些结构条件,但不需要f的凹性,建立了方程黏度解的外部存在唯一性结果。我们设置的方程可以包括著名的Monge-Amp 'ere方程,Hessian方程和Hessian商方程作为特殊情况。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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