A priori estimates of stable solutions of the general Hardy-Henon equation in the ball
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908424067874816 |
|---|---|
| author | Martinez-Baena, J. Silverio Villegas, Salvador |
| author_facet | Martinez-Baena, J. Silverio Villegas, Salvador |
| contents | This paper is devoted to the study of semi-stable radial solutions $u\in H^1(B_1)$ of $-Δu=\vert x\vert^αf(u) \mbox{ in } B_1\setminus\lbrace0\rbrace$, where $f\in C^1(\mathbb{R})$ is a general nonlinearity, $α>-2$ and $B_1$ is the unit ball of $\mathbb{R}^N$, $N>1$. We establish the boudness of such solutions for dimensions $2\leq N<10+4α$ and sharp pointwise estimates in the case $N\geq10+4α$. In addition, we provide, for this range of dimensions, a large family of semi-stable radially decreasing unbounded $H^1(B_1)$ solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21515 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A priori estimates of stable solutions of the general Hardy-Henon equation in the ball Martinez-Baena, J. Silverio Villegas, Salvador Analysis of PDEs 35B45, 35B35, 35J61 This paper is devoted to the study of semi-stable radial solutions $u\in H^1(B_1)$ of $-Δu=\vert x\vert^αf(u) \mbox{ in } B_1\setminus\lbrace0\rbrace$, where $f\in C^1(\mathbb{R})$ is a general nonlinearity, $α>-2$ and $B_1$ is the unit ball of $\mathbb{R}^N$, $N>1$. We establish the boudness of such solutions for dimensions $2\leq N<10+4α$ and sharp pointwise estimates in the case $N\geq10+4α$. In addition, we provide, for this range of dimensions, a large family of semi-stable radially decreasing unbounded $H^1(B_1)$ solutions. |
| title | A priori estimates of stable solutions of the general Hardy-Henon equation in the ball |
| topic | Analysis of PDEs 35B45, 35B35, 35J61 |
| url | https://arxiv.org/abs/2506.21515 |