Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.21162 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914218907795456 |
|---|---|
| author | Hou, Yongjun |
| author_facet | Hou, Yongjun |
| contents | Fix an integer $n\geq 2$, an exponent $1<p<\infty$, and a domain $Ω\subseteq\mathbb{R}^{n}$. Let $Ω^{*}\triangleqΩ\setminus\{\hat{x}\}$ where $\hat{x}\inΩ$. Under some further conditions, we construct optimal Hardy-weights for the Finsler $p$-Dirichlet integral $$Q_{0}[ϕ;Ω^{*}]\triangleq\int_{Ω^{*}}H(x,\nabla ϕ)^{p}\,\mathrm{d}x\quad \mbox{on}\quad C^{\infty}_{c}(Ω^{*}),$$ and the Finsler $p$-Dirichlet integral with a potential $$Q_{V}[ϕ;Ω]\triangleq\int_Ω\left(H(x,\nabla ϕ)^{p}+ V|ϕ|^{p}\right)\,\mathrm{d}x\quad \mbox{on}\quad C^{\infty}_{c}(Ω),$$where $H(x,\cdot)$ is a family of norms on $\mathbb{R}^{n}$ parameterized by $x\inΩ^{*}$ or $x\inΩ$, respectively, and the potential $V$ lies in a subspace $\widehat{M}^{q}_{\rm loc}(p;Ω)$ of a local Morrey space $M^{q}_{\rm loc}(p;Ω)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21162 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Hardy-weights for the Finsler $p$-Dirichlet integral with a potential Hou, Yongjun Analysis of PDEs 47J20 (Primary) 35B09, 35J20, 35J62, 35P30 (Secondary) Fix an integer $n\geq 2$, an exponent $1<p<\infty$, and a domain $Ω\subseteq\mathbb{R}^{n}$. Let $Ω^{*}\triangleqΩ\setminus\{\hat{x}\}$ where $\hat{x}\inΩ$. Under some further conditions, we construct optimal Hardy-weights for the Finsler $p$-Dirichlet integral $$Q_{0}[ϕ;Ω^{*}]\triangleq\int_{Ω^{*}}H(x,\nabla ϕ)^{p}\,\mathrm{d}x\quad \mbox{on}\quad C^{\infty}_{c}(Ω^{*}),$$ and the Finsler $p$-Dirichlet integral with a potential $$Q_{V}[ϕ;Ω]\triangleq\int_Ω\left(H(x,\nabla ϕ)^{p}+ V|ϕ|^{p}\right)\,\mathrm{d}x\quad \mbox{on}\quad C^{\infty}_{c}(Ω),$$where $H(x,\cdot)$ is a family of norms on $\mathbb{R}^{n}$ parameterized by $x\inΩ^{*}$ or $x\inΩ$, respectively, and the potential $V$ lies in a subspace $\widehat{M}^{q}_{\rm loc}(p;Ω)$ of a local Morrey space $M^{q}_{\rm loc}(p;Ω)$. |
| title | Optimal Hardy-weights for the Finsler $p$-Dirichlet integral with a potential |
| topic | Analysis of PDEs 47J20 (Primary) 35B09, 35J20, 35J62, 35P30 (Secondary) |
| url | https://arxiv.org/abs/2512.21162 |