Global Compactness Result for a Brézis-Nirenberg-Type Problem Involving Mixed Local Nonlocal Operator
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918016938147840 |
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| author | Chakraborty, Souptik Gupta, Diksha Malhotra, Shammi Sreenadh, Konijeti |
| author_facet | Chakraborty, Souptik Gupta, Diksha Malhotra, Shammi Sreenadh, Konijeti |
| contents | This paper investigates the profile decomposition of Palais-Smale sequences associated with a Brezis-Nirenberg type problem involving a combination of mixed local nonlocal operators, given by
\begin{equation*}
\left\{\begin{aligned}
&-Δu + (-Δ)^s u - λu = |u|^{2^*-2}u \;\;\mbox{ in } Ω,
&\quad u=0\,\mbox{ in }\mathbb{R}^N\setminus Ω.
\end{aligned}
\right.
\end{equation*} where $Ω\subseteq \mathbb{R}^{N}$ is a smooth bounded domain with $N \geq 3$, $s\in (0,1),\,λ\in\mathbb{R}$ is a real parameter and $2^* = \frac{2N}{N - 2} $ denotes the critical Sobolev exponent. As an application of the derived global compactness result, we further study the existence of positive solution of the corresponding Coron-type problem (C. R. Acad. Sci. Paris Sér I Math, 299(7):209-212, 1984) when $λ=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15968 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global Compactness Result for a Brézis-Nirenberg-Type Problem Involving Mixed Local Nonlocal Operator Chakraborty, Souptik Gupta, Diksha Malhotra, Shammi Sreenadh, Konijeti Analysis of PDEs Functional Analysis 35B33, 35B38, 35J20, 35J61 This paper investigates the profile decomposition of Palais-Smale sequences associated with a Brezis-Nirenberg type problem involving a combination of mixed local nonlocal operators, given by \begin{equation*} \left\{\begin{aligned} &-Δu + (-Δ)^s u - λu = |u|^{2^*-2}u \;\;\mbox{ in } Ω, &\quad u=0\,\mbox{ in }\mathbb{R}^N\setminus Ω. \end{aligned} \right. \end{equation*} where $Ω\subseteq \mathbb{R}^{N}$ is a smooth bounded domain with $N \geq 3$, $s\in (0,1),\,λ\in\mathbb{R}$ is a real parameter and $2^* = \frac{2N}{N - 2} $ denotes the critical Sobolev exponent. As an application of the derived global compactness result, we further study the existence of positive solution of the corresponding Coron-type problem (C. R. Acad. Sci. Paris Sér I Math, 299(7):209-212, 1984) when $λ=0$. |
| title | Global Compactness Result for a Brézis-Nirenberg-Type Problem Involving Mixed Local Nonlocal Operator |
| topic | Analysis of PDEs Functional Analysis 35B33, 35B38, 35J20, 35J61 |
| url | https://arxiv.org/abs/2504.15968 |