Corpus ID: 237571581

Quantitative H\"older Estimates for Even Singular Integral Operators on Patches

@inproceedings{Gancedo2021QuantitativeHE,
  title={Quantitative H\"older Estimates for Even Singular Integral Operators on Patches},
  author={Francisco Gancedo and Eduardo Garc{\'i}a-Ju{\'a}rez},
  year={2021}
}
Abstract. In this paper we show a constructive method to obtain new Cσ estimates of even singular integral operators on characteristic functions of domains with C regularity, 0 ă σ ă 1. This kind of functions were shown in first place to be bounded (classically only in the BMO space) to obtain global regularity for the vortex patch problem [2]. This property has then been applied to solve different type of problems in harmonic analysis and PDEs. Going beyond in regularity, the functions are… Expand
2 Citations
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References

SHOWING 1-10 OF 18 REFERENCES
Characterizing regularity of domains via the Riesz transforms on their boundaries
Given a domain D in R^d with mild geometric measure theoretic assumptions on its boundary, we show that boundedness of the principal value Riesz tranforms (witn kernel of homogeneity -(d-1)) onExpand
Estimates for the maximal singular integral in terms of the singular integral:the case of even kernels
The purpose of this paper is to describe the smooth homogeneous Calderon-Zygmund operators for which the maximal singular integral T*f may be controlled by the singular integral Tf. We consider twoExpand
Global Regularity of 2D Navier-Stokes Free Boundary with Small Viscosity Contrast
This paper studies the dynamics of two incompressible immiscible fluids in 2D modeled by the inhomogeneous Navier-Stokes equations. We prove that if initially the viscosity contrast is small thenExpand
Extra cancellation of even Calderón–Zygmund operators and quasiconformal mappings
Abstract In this paper we discuss a special class of Beltrami coefficients whose associated quasiconformal mapping is bilipschitz. A particular example are those of the form f ( z ) χ Ω ( z ) , whereExpand
Global Regularity of 2D Density Patches for Inhomogeneous Navier–Stokes
This paper is about Lions’ open problem on density patches (Lions in Mathematical topics in fluid mechanics. Vol. 1, volume 3 of Oxford Lecture series in mathematics and its applications, ClarendonExpand
Striated Regularity of 2-D Inhomogeneous Incompressible Navier–Stokes System with Variable Viscosity
  • M. Paicu, P. Zhang
  • Physics, Mathematics
  • Communications in Mathematical Physics
  • 2019
In this paper, we investigate the global existence and uniqueness of strong solutions to 2D incompressible inhomogeneous Navier–Stokes equations with viscous coefficient depending on the density andExpand
Regularity Results for Viscous 3D Boussinesq Temperature Fronts
This paper is about the dynamics of non-diffusive temperature fronts evolving by the incompressible viscous Boussinesq system in $${\mathbb {R}}^3$$ R 3 . We provide local in time existence resultsExpand
Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals
PrefaceGuide to the ReaderPrologue3IReal-Variable Theory7IIMore About Maximal Functions49IIIHardy Spaces87IVH[superscript 1] and BMO139VWeighted Inequalities193VIPseudo-Differential and SingularExpand
On the splash singularity for the free-surface of a Navier–Stokes fluid
  • D. Coutand, S. Shkoller
  • Mathematics, Physics
  • Annales de l'Institut Henri Poincaré C, Analyse non linéaire
  • 2019
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. We prove that for $d$-dimensional flows, $d=2$ or $3$, the free-surface of aExpand
Splash Singularities for the Free Boundary Navier-Stokes Equations
In this paper, we prove the existence of smooth initial data for the 2D free boundary incompressible Navier-Stokes equations, for which the smoothness of the interface breaks down in finite time intoExpand
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