Hardy's Inequality for the fractional powers of Grushin operator
, 2016 We prove Hardy's inequality for the fractional powers of the generalized sublaplacian and the fractional powers of the Grushin operator. We also find an integral representation and a ground state representation for the fractional powers of generalized ...
Boris-Marko Kukovec (2131279) +2 more
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Besov regularity for solutions of p-harmonic equations
Advances in Nonlinear Analysis, 2017 We establish the higher fractional differentiability of the solutions to nonlinear elliptic equations in divergence form, i.e., div𝒜(x,Du)=divF,{\operatorname{div}\mathcal{A}(x,Du)=\operatorname{div}F,} when 𝒜{\mathcal{A}} is a p-harmonic type ...
Clop Albert +2 more
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$L^p-L^q$ estimates for maximal operators associated to families of finite type curves
, 2020 We study the boundedness problem for maximal operators $\mathbb{M}$ associated to averages along families of finite type curves in the plane, defined by $$\mathbb{M}f(x) \, := \, \sup_{1 \leq t \leq 2} \left|\int_{\mathbb{C}} f(x-ty) \, \rho(y) \, d ...
Manna, Ramesh
core
A Data-Driven Edge-Preserving D-bar Method for Electrical Impedance Tomography
, 2014 In Electrical Impedance Tomography (EIT), the internal conductivity of a body is recovered via current and voltage measurements taken at its surface.
Hamilton, Sarah +2 more
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Analyticity and Existence of the Keller–Segel–Navier–Stokes Equations in Critical Besov Spaces
Advanced Nonlinear Studies, 2018 This paper deals with the Cauchy problem to the Keller–Segel model coupled with the incompressible 3-D Navier–Stokes equations. Based on so-called Gevrey regularity estimates, which are motivated by the works of Foias and Temam [20], we prove that the ...
Yang Minghua, Fu Zunwei, Liu Suying
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Well/ill-posedness for the dissipative Navier–Stokes system in generalized Carleson measure spaces
Advances in Nonlinear Analysis, 2017 As an essential extension of the well known case β∈(12,1]{\beta\kern-1.0pt\in\kern-1.0pt({\frac{1}{2}},1]} to the hyper-dissipative case β∈(1,∞){\beta\kern-1.0pt\in\kern-1.0pt(1,\infty)}, this paper establishes both well-posedness and ill-posedness (not ...
Wang Yuzhao, Xiao Jie
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The Neumann function and the L p Neumann problem in chord-arc domains
Advanced Nonlinear StudiesWe construct the Neumann function in a 1-sided chord-arc domain (i.e., a uniform domain with an Ahlfors regular boundary), and establish size and Hölder continuity estimates up to the boundary.
Hofmann Steve, Sparrius Derek
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Some remarks on Riesz transforms on exterior Lipschitz domains
Forum of Mathematics, SigmaLet $n\ge 2$ and $\mathcal {L}=-\mathrm {div}(A\nabla \cdot )$ be an elliptic operator on $\mathbb {R}^n$ . Given an exterior Lipschitz domain $\Omega $ , let $\mathcal {L}_D$ be the elliptic operator $\mathcal {L}$
Renjin Jiang, Sibei Yang
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Quadratic estimates for perturbed Dirac type operators on doubling measure metric spaces [PDF]
, 2011 We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these operators have a ...
Bandara, Lashi
core
Green function estimates on complements of low-dimensional uniformly rectifiable sets. [PDF]
Math Ann, 2023 David G, Feneuil J, Mayboroda S.
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