Results 61 to 70 of about 4,782 (151)
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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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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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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Global hypoellipticity of planar complex vector fields
Journal of Differential Equations, 2019 We study the global hypoellipticity property for non-singular planar complex vector fields. The results obtained are related to condition ( P ) of Nirenberg-Treves and the boundedness of certain subsets of the plane where the real and the imaginary parts
A. Bergamasco, Renato A. Laguna, S. Zani
semanticscholar +1 more source
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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Pseudodifferential operators with generalized symbols and regularity theory
Electronic Journal of Differential Equations, 2005 We study pseudodifferential operators with amplitudes $a_varepsilon (x,xi)$ depending on a singular parameter $varepsilon o 0$ with asymptotic properties measured by different scales.
Claudia Garetto +2 more
doaj
Elliptic regularity and solvability for partial differential equations with Colombeau coefficients
Electronic Journal of Differential Equations, 2004 This paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau.
Gunther Hormann +1 more
doaj
Spectral Properties of Hypoelliptic Operators [PDF]
Communications in Mathematical Physics, 2003 We study hypoelliptic operators with polynomially bounded coefficients that are of the form K = sum_{i=1}^m X_i^T X_i + X_0 + f, where the X_j denote first order differential operators, f is a function with at most polynomial growth, and X_i^T denotes the formal adjoint of X_i in L^2.
Eckmann, J.-P., Hairer, M.
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Global Hypoellipticity and Liouville Numbers [PDF]
Proceedings of the American Mathematical Society, 1972 We consider global hypoellipticity of constant coefficient differential operators on the 2-torus, and prove that it is equivalent to an algebraic growth condition on the symbol. This is applied to give necessary and sufficient conditions that a constant coefficient vector field be globally hypoelliptic.
Greenfield, Stephen J. +1 more
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