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Gevrey class regularity for parabolic equations
Differential and Integral Equations, 2001 We consider the regularity of parabolic equations. We obtain that the solution belongs to Gevrey class 2 up to the boundary if functions in the equation belong to Gevrey class 2 in all dependent variables.
Lee, Pei-Ling, Guo, Yung-Jen Lin
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Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules [PDF]
, 2015 It has long been suspected that the non-cutoff Boltzmann operator has similar coercivity properties as a fractional Laplacian. This has led to the hope that the homogenous Boltzmann equation enjoys similar regularity properties as the heat equation with ...
Barbaroux, Jean-Marie +3 more
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On Gevrey solvability and regularity [PDF]
Mathematische Nachrichten, 2009 AbstractIn this paper we study global C∞ and Gevrey solvability for a class of sublaplacian defined on the torus T3. We also prove Gevrey regularity for a class of solutions of certain operators that are globally C∞ hypoelliptic in the N ‐dimensional torus (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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Gevrey class regularity of the magnetohydrodynamics equations [PDF]
The ANZIAM Journal, 2002 AbstractIn this article, we use the method of Foias and Temam to show that the strong solutions of the time-dependent magnetohydrodynamics equations in a periodic domain are analytic in time with values in a Gevrey class of functions. As immediate corollaries we find that the solutions are analytic in Hr-norms and that the solutions become smooth ...
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Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation [PDF]
, 2015 We consider the spatially inhomogeneous non-cutoff Kac's model of the Boltzmann equation. We prove that the Cauchy problem for the fluctuation around the Maxwellian distribution enjoys Gelfand-Shilov regularizing properties with respect to the velocity ...
Lerner, Nicolas +3 more
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Gevrey regularity for integro-differential operators
Journal of Mathematical Analysis and Applications, 2015 We prove a regularity theory in the Gevrey class for a family of nonlocal differential equations of elliptic type.
G. Albanese, A. Fiscella, E. Valdinoci
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Boundary Values in Ultradistribution Spaces Related to Extended Gevrey Regularity [PDF]
Mathematics, 2020 Following the well-known theory of Beurling and Roumieu ultradistributions, we investigate new spaces of ultradistributions as dual spaces of test functions which correspond to associated functions of logarithmic-type growth at infinity. In the given framework we prove that boundary values of analytic functions with the corresponding logarithmic growth
Stevan Pilipović +2 more
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On 𝐶^{∞} and Gevrey regularity of sublaplacians [PDF]
Transactions of the American Mathematical Society, 2006 In this paper we consider zero order perturbations of a class of sublaplacians on the two-dimensional torus and give sufficient conditions for global C ∞ C^\infty regularity to persist. In the case of analytic coefficients, we prove Gevrey regularity for a general class of sublaplacians when the finite type condition
A. Himonas, Gerson Petronilho
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Analytical regularizing effect for the radial and spatially homogeneous Boltzmann equation [PDF]
, 2012 In this paper, we consider a class of spatially homogeneous Boltzmann equation without angular cutoff.
Glangetas, Léo, Najeme, Mohamed
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Extended Gevrey Regularity via the Short-Time Fourier Transform [PDF]
, 2020 We study the regularity of smooth functions whose derivatives are dominated by sequences of the form $M_p^{ ,\s}=p^{ p^{\s}}$, $ >0$, $\s\geq1$. We show that such functions can be characterized through the decay properties of their short-time Fourier transforms (STFT), and recover \cite[Theorem 3.1]{CNR} as the special case when $ \t>1$ and ...
Teofanov, Nenad, Tomić, Filip
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