Results 41 to 50 of about 3,513,590 (164)
Global Gevrey hypoellipticity on the torus for a class of systems of complex vector fields
, 2018 Let $L_j = \partial_{t_j} + (a_j+ib_j)(t_j) \partial_x, \, j = 1, \dots, n,$ be a system of vector fields defined on the torus $\mathbb{T}_t^{n}\times\mathbb{T}_x^1$, where the coefficients $a_j$ and $b_j$ are real-valued functions belonging to the ...
de Medeira, Cleber +2 more
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Rough hypoellipticity for the heat equation in Dirichlet spaces
Mathematische Nachrichten, 2023 AbstractThis paper aims at proving the local boundedness and continuity of solutions of the heat equation in the context of Dirichlet spaces under some rather weak additional assumptions. We consider symmetric local regular Dirichlet forms, which satisfy mild assumptions concerning (1) the existence of cut‐off functions, (2) a local ultracontractivity ...
Qi Hou, Laurent Saloff‐Coste
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${L^p}$-Liouville Theorems for Invariant Partial Differential Operators in ${\mathbb{R}^n}$
, 2014 We prove some $L^p$-Liouville theorems for hypoelliptic second order Partial Differential Operators left translation invariant with respect to a Lie group composition law in $\mathbb{R}^n$.
Kogoj, Alessia E., Lanconelli, Ermanno
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A Parametrix for Step-Two Hypoelliptic Diffusion Equations [PDF]
Transactions of the American Mathematical Society, 1986 In this paper I construct a parametrix for the hypoelliptic diffusion equations ( ∂ / ∂ t − L ) u = 0 (\partial /\partial t - L)u = 0 , where L = ∑ a = 1 n
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Inverse source problems for positive operators. I: Hypoelliptic diffusion and subdiffusion equations [PDF]
Journal of Inverse and Ill-Posed Problems, 2018 A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered.
Michael Ruzhansky +2 more
semanticscholar +1 more source
The Gevrey hypoellipticity for kinetic equations
, 2011 In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.
Chen, Hua, Li, Weixi, Xu, Chao-Jiang
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On the completeness of the space OC$\mathcal {O}_C$
Mathematische Nachrichten, Volume 298, Issue 8, Page 2740-2748, August 2025.Abstract We explicitly prove the compact regularity of the LF$\mathcal {LF}$‐space of double sequences limk→(s⊗̂(ℓp)k)≅limk→(s⊗̂(c0)−k)$ {\lim _{k\rightarrow }} (s\widehat{\otimes }(\ell ^p)_{k}) \cong {\lim _{k\rightarrow }}(s\widehat{\otimes }(c_0)_{-k})$, 1≤p≤∞$1\le p\le \infty$.
Michael Kunzinger, Norbert Ortner
wiley +1 more source
A Theory of Generalized Coordinates for Stochastic Differential Equations
Studies in Applied Mathematics, Volume 154, Issue 5, May 2025.ABSTRACT Stochastic differential equations are ubiquitous modeling tools in applied mathematics and the sciences. In most modeling scenarios, random fluctuations driving dynamics or motion have some nontrivial temporal correlation structure, which renders the SDE non‐Markovian; a phenomenon commonly known as ‘colored’’ noise.
Lancelot Da Costa +7 more
wiley +1 more source
On a rigidity result for Kolmogorov-type operators
Bruno Pini Mathematical Analysis SeminarLet D be a bounded open subset of ℝN and let z0 be a point of D. Assume that the Newtonian potential of D is proportional outside D to the potential of a mass concentrated at z0. Then D is a Euclidean ball centred at z0. This theorem, proved by Aharonov,
Alessia E. Kogoj
doaj +1 more source