Results 31 to 40 of about 154 (95)
Local Hypoellipticity by Lyapunov Function
Abstract and Applied Analysis, Volume 2016, Issue 1, 2016., 2016 We treat the local hypoellipticity, in the first degree, for a class of abstract differential operators complexes; the ones are given by the following differential operators: Lj = ∂/∂tj + (∂ϕ/∂tj)(t, A)A, j = 1,2, …, n, where A : D(A) ⊂ H → H is a self‐adjoint linear operator, positive with 0 ∈ ρ(A), in a Hilbert space H, and ϕ = ϕ(t, A) is a series of
E. R. Aragão-Costa, Maria Grazia Naso
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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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A proof of hypoellipticity for Kohn’s operator via FBI
, 2011 A new proof of both analytic and C∞ hypoellipticity of Kohn's operator is given using FBI techniques introduced by J. Sjöstrand.
Chinni G., Gregorio Chinni
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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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The Metivier inequality and ultradifferentiable hypoellipticity
, 2023 In 1980 M{\'e}tivier characterized the analytic (and Gevrey) hypoellipticity of $L^2$-solvable partial linear differential operators by a-priori estimates.
Fürdös, Stefan, Cordaro, Paulo D.
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On global analytic and Gevrey hypoellipticity on the torus and the M??tivier inequality
, 2016 We obtain a global version in the N-dimensional torus of the Metivier inequality for analytic and Gevrey hypoellipticity, and based on it we introduce a class of globally analytic hypoelliptic operators which remain so after suitable lower order ...
P. D. Cordaro, G. Chinni
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Hyperfunctions and (analytic) hypoellipticity
, 2009 In this work we discuss the problem of smooth and analytic regularity for hyperfunction solutions to linear partial differential equations with analytic coefficients.
HANGES, Nicholas, CORDARO, Paulo D.
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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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Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators [PDF]
, 2003 summary:The problems of Gevrey hypoellipticity for a class of degenerated quasi-elliptic operators are studied by several authors (see [1]--[5]). In this paper we obtain the Gevrey hypoellipticity for a degenerated quasi-elliptic operator in $\Bbb R^2 ...
Margaryan, V. N., Hakobyan, G. O.
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