外域上全非线性方程解的渐近性质

IF 0.8 4区数学 Q2 MATHEMATICS

Comptes Rendus Mathematique Pub Date : 2021-01-25 DOI:10.5802/CRMATH.138

Xiaobiao Jia

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引用次数: 3

摘要

本文考虑了一类完全非线性椭圆方程F (D2u) = F (x)在外域上解在无穷远处的渐近性，其中Hessian矩阵(D2u)在无穷远处趋向于某个对称正定矩阵，F (x)在无穷远处= O(|x|−t)，且尖锐条件为t |。此外，当(D2u)仅在无穷远处非常接近某个对称正定矩阵时，我们也得到了同样的结果。2020数学学科分类。35J60, 35B40。2020年9月4日收稿，2020年10月9日改稿，2020年10月25日收稿。

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Asymptotic behavior of solutions of fully nonlinear equations over exterior domains

In this paper, we consider the asymptotic behavior at infinity of solutions of a class of fully nonlinear elliptic equations F (D2u) = f (x) over exterior domains, where the Hessian matrix (D2u) tends to some symmetric positive definite matrix at infinity and f (x) = O(|x|−t ) at infinity with sharp condition t > 2. Moreover, we also obtain the same result if (D2u) is only very close to some symmetric positive definite matrix at infinity. 2020 Mathematics Subject Classification. 35J60, 35B40. Manuscript received 4th September 2020, revised 9th October 2020, accepted 25th October 2020.

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来源期刊

Comptes Rendus Mathematique 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

115

审稿时长

16.6 weeks

期刊介绍： The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, … Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English. The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.