Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2603.02920 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914365336190976 |
|---|---|
| author | de Almeida, Marcelo F. Filho, Edilson P. dos Santos |
| author_facet | de Almeida, Marcelo F. Filho, Edilson P. dos Santos |
| contents | We prove a parabolic analogue of Wolff's inequality adapted to the intrinsic scaling $δ_c(x,t)=(cx,c^2t)$ and formulated in terms of time-backward parabolic dyadic rectangles. As a consequence, we obtain equivalent characterizations of parabolic $(α,q)$-thinness in this geometric setting and establish the associated Kellogg and Choquet properties. We further use the notion of $(α,2)$-thinness defined in terms of fractional heat balls and prove that the sets of irregular boundary points $z_0\in\partialΩ$ for the heat operator $\partial_t-Δ$ and for the degenerate operator $\mathscr{L}a=\partial_t(|y|^a\cdot)-\operatorname{div}(|y|^a\nabla\cdot)$ in $Ω\subset\mathbb{R}^{d+1}$ are negligible with respect to the thermal capacity $\mathrm{cap}^{\mathcal T}$ and the parabolic Bessel capacity $C_{α,2}$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_02920 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear parabolic thin sets and parabolic Wolff inequalities de Almeida, Marcelo F. Filho, Edilson P. dos Santos Analysis of PDEs 31C45, 31B15, 31C40, 42B37 We prove a parabolic analogue of Wolff's inequality adapted to the intrinsic scaling $δ_c(x,t)=(cx,c^2t)$ and formulated in terms of time-backward parabolic dyadic rectangles. As a consequence, we obtain equivalent characterizations of parabolic $(α,q)$-thinness in this geometric setting and establish the associated Kellogg and Choquet properties. We further use the notion of $(α,2)$-thinness defined in terms of fractional heat balls and prove that the sets of irregular boundary points $z_0\in\partialΩ$ for the heat operator $\partial_t-Δ$ and for the degenerate operator $\mathscr{L}a=\partial_t(|y|^a\cdot)-\operatorname{div}(|y|^a\nabla\cdot)$ in $Ω\subset\mathbb{R}^{d+1}$ are negligible with respect to the thermal capacity $\mathrm{cap}^{\mathcal T}$ and the parabolic Bessel capacity $C_{α,2}$, respectively. |
| title | Nonlinear parabolic thin sets and parabolic Wolff inequalities |
| topic | Analysis of PDEs 31C45, 31B15, 31C40, 42B37 |
| url | https://arxiv.org/abs/2603.02920 |