تقرير
Differential equations defined by Kre\u{\i}n-Feller operators on Riemannian manifolds
| العنوان: | Differential equations defined by Kre\u{\i}n-Feller operators on Riemannian manifolds |
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| المؤلفون: | Ngai, Sze-Man, Ouyang, Lei |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis |
| الوصف: | We study linear and semi-linear wave, heat, and Schr\"odinger equations defined by Kre\u{\i}n-Feller operator $-\Delta_\mu$ on a complete Riemannian $n$-manifolds $M$, where $\mu$ is a finite positive Borel measure on a bounded open subset $\Omega$ of $M$ with support contained in $\overline{\Omega}$. Under the assumption that $\underline{\operatorname{dim}}_{\infty}(\mu)>n-2$, we prove that for a linear or semi-linear equation of each of the above three types, there exists a unique weak solution. We study the crucial condition $\dim_(\mu)>n-2$ and provide examples of measures on $\mathbb{S}^2$ and $\mathbb{T}^2$ that satisfy the condition. We also study weak solutions of linear equations of the above three classes by using examples on $\mathbb{S}^1$ Comment: 35 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2408.04858 |
| رقم الأكسشن: | edsarx.2408.04858 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |