Zobrazeno 1 - 10
of 209
pro vyhledávání: '"Vita Stefano"'
We provide fine asymptotics of solutions of fractional elliptic equations at boundary points where the domain is locally conical; that is, corner type singularities appear. Our method relies on a suitable smoothing of the corner singularity and an ap
Externí odkaz:
http://arxiv.org/abs/2405.12718
Autor:
Vita, Stefano
Let $\Omega\subset\mathbb R^2$ be a chord arc domain. We give a simple proof of the the following fact, which is commonly known to be true: a nontrivial harmonic function which vanishes continuously on a relatively open set of the boundary cannot hav
Externí odkaz:
http://arxiv.org/abs/2405.04388
We prove $\textit{a priori}$ and $\textit{a posteriori}$ H\"older bounds and Schauder $C^{1,\alpha}$ estimates for continuous solutions to singular/degenerate equations with variable coefficients of type $$ \mathrm{div}\left(|u|^a A\nabla w\right)=0\
Externí odkaz:
http://arxiv.org/abs/2404.06980
In this paper, we complete the analysis initiated in [AFV24] establishing some higher order $C^{k+2,\alpha}$ Schauder estimates ($k \in \mathbb{N}$) for a a class of parabolic equations with weights that are degenerate/singular on a characteristic hy
Externí odkaz:
http://arxiv.org/abs/2403.08575
Publikováno v:
Calc. Var. Partial Differential Equations 63-8 (2024), 1-46
We establish some $C^{0,\alpha}$ and $C^{1,\alpha}$ regularity estimates for a class of weighted parabolic problems in divergence form. The main novelty is that the weights may vanish or explode on a characteristic hyperplane $\Sigma$ as a power $a >
Externí odkaz:
http://arxiv.org/abs/2401.06038
Publikováno v:
Calc. Var. Partial Differential Equations 63-9 (2024), 1-42
In this paper, we study degenerate or singular elliptic equations in divergence form $$-\text{div}(x_n^\alpha A\nabla u)=\text{div}(x_n^\alpha \mathbf{g})\quad\text{in }B_1\cap\{x_n>0\}.$$ When $\alpha>-1$, we establish boundary Schauder type estimat
Externí odkaz:
http://arxiv.org/abs/2311.06846
Publikováno v:
Advances in Nonlinear Analysis, Vol 4, Iss 2, Pp 91-107 (2015)
In this note, we will study the problem (-Δ)psu = f(x) on Ω, u = 0 in ℝN∖Ω, where 0 < s < 1, (-Δ)ps is the nonlocal p-Laplacian defined below, Ω is a smooth bounded domain. The main point studied in this work is to prove, adapting the techni
Externí odkaz:
https://doaj.org/article/14edc666abcc4a728ba0ac8175e36b1d
Autor:
Jeon, Seongmin, Vita, Stefano
Publikováno v:
J. Differential Equations 412 (2024), 808-856
Aim of this paper is to provide higher order boundary Harnack principles [De Silva-Savin 15] for elliptic equations in divergence form under Dini type regularity assumptions on boundaries, coefficients and forcing terms. As it was proven in [Terracin
Externí odkaz:
http://arxiv.org/abs/2305.05535
Publikováno v:
Arch. Ration. Mech. Anal. 248-2 (2024), 1-44
As a first result we prove higher order Schauder estimates for solutions to singular/degenerate elliptic equations of type: \[ -\mathrm{div}\left(\rho^aA\nabla w\right)=\rho^af+\mathrm{div}\left(\rho^aF\right) \quad\textrm{in}\; \Omega \] for exponen
Externí odkaz:
http://arxiv.org/abs/2301.00227