Strict Faber-Krahn type inequality for the mixed local-nonlocal operator under polarization
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915316181762048 |
|---|---|
| author | Kumar, K Ashok Biswas, Nirjan |
| author_facet | Kumar, K Ashok Biswas, Nirjan |
| contents | Let $Ω\subset \mathbb{R}^d$ with $d\geq 2$ be a bounded domain of class $\mathcal{C}^{1,β}$ for some $β\in (0,1)$. For $p\in (1, \infty )$ and $s\in (0,1)$, let $Λ^s_{p}(Ω)$ be the first eigenvalue of the mixed local-nonlocal operator $-Δ_p+(-Δ_p)^s$ in $Ω$ with the homogeneous nonlocal Dirichlet boundary condition. We establish a strict Faber-Krahn type inequality for $Λ_{p}^s(\cdot )$ under polarization. As an application of this strict inequality, we obtain the strict monotonicity of $Λ_{p}^s(\cdot )$ over annular domains and characterize the rigidity property of the balls in the classical Faber-Krahn inequality for $-Δ_p+(-Δ_p)^s$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07520 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strict Faber-Krahn type inequality for the mixed local-nonlocal operator under polarization Kumar, K Ashok Biswas, Nirjan Analysis of PDEs Primary 35R11, 49Q10, Secondary 35B51, 47J10 Let $Ω\subset \mathbb{R}^d$ with $d\geq 2$ be a bounded domain of class $\mathcal{C}^{1,β}$ for some $β\in (0,1)$. For $p\in (1, \infty )$ and $s\in (0,1)$, let $Λ^s_{p}(Ω)$ be the first eigenvalue of the mixed local-nonlocal operator $-Δ_p+(-Δ_p)^s$ in $Ω$ with the homogeneous nonlocal Dirichlet boundary condition. We establish a strict Faber-Krahn type inequality for $Λ_{p}^s(\cdot )$ under polarization. As an application of this strict inequality, we obtain the strict monotonicity of $Λ_{p}^s(\cdot )$ over annular domains and characterize the rigidity property of the balls in the classical Faber-Krahn inequality for $-Δ_p+(-Δ_p)^s$. |
| title | Strict Faber-Krahn type inequality for the mixed local-nonlocal operator under polarization |
| topic | Analysis of PDEs Primary 35R11, 49Q10, Secondary 35B51, 47J10 |
| url | https://arxiv.org/abs/2309.07520 |