Results 31 to 40 of about 125 (119)
Journal of the London Mathematical Society, Volume 110, Issue 5, November 2024.Abstract The aim of this paper is to prove the existence of Hadamard states for the Maxwell equations on any globally hyperbolic spacetime. This will be achieved by introducing a new gauge fixing condition, the Cauchy radiation gauge, that will allow to suppress all the unphysical degrees of freedom. The key ingredient for achieving this gauge is a new
Simone Murro, Gabriel Schmid
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Hypoellipticity: Geometrization and speculation [PDF]
, 2000 To any finite collection of smooth real vector fields $X_j$ in $\reals^n$ we associate a metric in the phase space $T^*\reals^n$. The relation between the asymptotic behavior of this metric and hypoellipticity of $\sum X_j^2$, in the smooth, real analytic, and Gevrey categories, is explored.
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On curvature bounds in Lorentzian length spaces
Journal of the London Mathematical Society, Volume 110, Issue 2, August 2024.Abstract We introduce several new notions of (sectional) curvature bounds for Lorentzian pre‐length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) time separation function, and, on the other hand, we study four‐point conditions, which are suitable also for the non‐intrinsic setting. Via these concepts, we are able
Tobias Beran +2 more
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Bulletin of the London Mathematical Society, Volume 56, Issue 3, Page 981-1003, March 2024.Abstract We study the linear relaxation Boltzmann equation on the torus with a spatially varying jump rate which can be zero on large sections of the domain. In Bernard and Salvarani (Arch. Ration. Mech. Anal. 208 (2013), no. 3, 977–984), Bernard and Salvarani showed that this equation converges exponentially fast to equilibrium if and only if the jump
Josephine Evans, Iván Moyano
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The Cheeger problem in abstract measure spaces
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract We consider nonnegative σ$\sigma$‐finite measure spaces coupled with a proper functional P$P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space perimeter ...
Valentina Franceschi +3 more
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Periodic Homogenization for Hypoelliptic Diffusions [PDF]
Journal of Statistical Physics, 2004 We study the long time behavior of an Ornstein-Uhlenbeck process under the influence of a periodic drift. We prove that, under the standard diffusive rescaling, the law of the particle position converges weakly to the law of a Brownian motion whose covariance can be expressed in terms of the solution of a Poisson equation.
Hairer, M., Pavliotis, G. A.
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A Necessary Condition For Analytic Hypoellipticity [PDF]
Mathematical Research Letters, 1994 The author continues his careful study of the analytic hypoellipticity of Hörmander's Laplacians. He considers here two real linearly independent analytic vector fields \(X_1\), \(X_2\) defined in an open set \(\Omega\subset \mathbb{R}^3\) such that the Hörmander's condition is satisfied (that is that the Lie algebra generated by \(X_1\) and \(X_2 ...
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Hypoellipticity in the complexes of pseudodifferential operators [PDF]
Proceedings of the American Mathematical Society, 1978 Sufficient conditions for the pseudodifferential operator defined on a complex to be hypoelliptic are investigated.
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The hypoelliptic Laplacian on the cotangent bundle [PDF]
Journal of the American Mathematical Society, 2005 In this paper, we construct a new version of Hodge theory, where the corresponding Laplacian acts on the total space of the cotangent bundle. This Laplacian is a hypoelliptic operator, which is in general non-self-adjoint. When properly interpreted, it provides an interpolation between classical Hodge theory and the generator of the geodesic flow.
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Hopf bifurcation without parameters in deterministic and stochastic modeling of cancer virotherapy, part II. [PDF]
J Math Anal Appl, 2022 Phan TA, Tian JP.
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