Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations

IF 3.1 1区数学 Q1 MATHEMATICS Communications on Pure and Applied Mathematics Pub Date : 2023-07-21 DOI:10.1002/cpa.22132

Alessio Figalli, Yi Ru-Ya Zhang

引用次数: 1

Abstract

We consider finite Morse index solutions to semilinear elliptic questions, and we investigate their smoothness. It is well-known that:

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超临界椭圆型方程有限Morse指数解的一致有界性

我们考虑了半线性椭圆型问题的有限Morse指数解，并研究了它们的光滑性。众所周知：-对于$n=2$，存在Morse指数$1$解，其$L^\infty$范数为无穷大。-对于$n\geq3$，幂型非线性的一致有界性在亚临界情况下成立，而对于临界非线性，Morse指数的有界性不能阻止$L^\infty$中的爆破。在本文中，我们研究了凸域内一般超临界非线性的情况，并证明了在锐维范围$3\leqn\leq9$中有限Morse指数解的内部先验$L^\infty$界。作为推论，我们得到了通过连续性方法构造的Gelfand问题的有限Morse指数解的一致界。

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

Communications on Pure and Applied Mathematics 数学-数学

CiteScore

6.70

自引率

3.30%

发文量

审稿时长

>12 weeks

期刊介绍： Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.