Results 31 to 40 of about 107 (95)
Remarks about global analytic hypoellipticity [PDF]
Transactions of the American Mathematical Society, 1999 We present a characterization of the operators \[ L = ∂
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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
Mathematische Nachrichten, Volume 297, Issue 7, Page 2517-2531, July 2024.Abstract In 1980, Métivier characterized the analytic (and Gevrey) hypoellipticity of L2$L^2$‐solvable partial linear differential operators by a priori estimates. In this note, we extend this characterization to ultradifferentiable hypoellipticity with respect to Denjoy–Carleman classes given by suitable weight sequences. We also discuss the case when
Paulo D. Cordaro, Stefan Fürdös
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Hypoellipticity and Non Hypoellipticity for Sums of Squares of Complex Vector Fields
Bruno Pini Mathematical Analysis Seminar, 2011 In this talk we give a report on a paper where we consider a model sum of squares of planar complex vector fields, being close to Kohn's operator but with a point singularity.
Antonio Bove
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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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Quasi-analyticity for hypoelliptic operators
Journal of Differential Equations, 1985 Let MP, p = 0, 1, 2 ,..., be a sequence of positive numbers satisfying the conditions (2.1)-(2.3). Let Sz be an open set in R”, and let 9((M,), s2) and 9( { M,}, Q), Sz z [w”, denote the test function spaces of Beurling type and Roumieu type of ultradifferentiable functions of compact support, respectively.
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Global analytic hypoellipticity and pseudoperiodic functions
Matemática Contemporânea, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Adalberto Bergamasco +2 more
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Failure of analytic hypoellipticity in a class of PDOs
, 2002 For the hypoelliptic differential operators $P={\partial^2_ x}+(x^k\partial_ y -x^l{\partial_t})^2$ introduced by T. Hoshiro, generalizing a class of M. Christ, in the cases of $k$ and $l$ left open in the analysis, the operators $P$ also fail to be {\em{analytic}} hypoelliptic (except for $(k,l)=(0,1)$), in accordance with Treves' conjecture.
Costin, O, Costin, R D
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On local and global analytic and Gevrey hypoellipticity [PDF]
Journées équations aux dérivées partielles, 1995 Some recent results in the investigation of analytic and Gevrey hypoellipticity of linear partial differential operators having analytic coefficients are formulated. Global analytic hypoellipticity is also studied. The analysis proposed here depends on certain nonlinear eigenvalue problems for ordinary differential equations. No proofs are given.
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