Large solutions of elliptic semilinear equations non-degenerate near the boundary

IF 1 3区 数学 Q1 MATHEMATICS Communications on Pure and Applied Analysis Pub Date : 2022-10-31 DOI:10.3934/cpaa.2023006
G. Díaz
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引用次数: 1

Abstract

In this paper we study the so-called large solutions of elliptic semilinear equations with non null sources term, thus solutions blowing up on the boundary of the domain for which reason they are greater than any other solution whenever Weak Maximum Principle holds. The main topic about large solutions is uniqueness results and their behavior near the boundary. It is much less than being simple. The structure of the semilinear equations considered includes the well known Keller-Osserman integral and an assumption on the ellipticity of the leading part of the differential operator. In our study an uniform ellipticity near the boundary is required. We consider source terms in the PDE whose boundary explosion is consistent with the Keller-Osserman condition. Extra Keller-Osserman explosions on the source are also studied, showing in particular that in some cases the PDE only admits large solutions.
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椭圆型半线性方程在边界附近非退化的大解
本文研究了具有非零源项的椭圆型半线性方程的所谓大解,当弱极大值原理成立时,解在边界上爆开,因此它们比其他任何解都大。大解的主要问题是解的唯一性结果及其在边界附近的行为。这远不如简单。所考虑的半线性方程的结构包括众所周知的Keller-Osserman积分和微分算子前导部分的椭圆性假设。在我们的研究中,边界附近需要一个均匀的椭圆性。我们考虑边界爆炸符合Keller-Osserman条件的偏微分方程中的源项。对源上额外的Keller-Osserman爆炸也进行了研究,特别表明在某些情况下PDE只允许大的解。
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来源期刊
CiteScore
1.90
自引率
10.00%
发文量
124
审稿时长
4-8 weeks
期刊介绍: CPAA publishes original research papers of the highest quality in all the major areas of analysis and its applications, with a central theme on theoretical and numeric differential equations. Invited expository articles are also published from time to time. It is edited by a group of energetic leaders to guarantee the journal''s highest standard and closest link to the scientific communities.
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