Results 1 to 10 of about 107 (95)
Analytic hypoellipticity of Keldysh operators [PDF]
Proceedings of the London Mathematical Society, 2021 We consider Keldysh-type operators, $ P = x_1 D_{x_1}^2 + a (x) D_{x_1} + Q (x, D_{x'} ) $, $ x = ( x_1, x') $ with analytic coefficients, and with $ Q ( x, D_{x'} ) $ second order, principally real and elliptic in $ D_{x'} $ for $ x $ near zero. We show that if $ P u =f $, $ u \in C^\infty $, and $ f $ is analytic in a neighbourhood of $ 0 $ then $ u $
Galkowski, J, Zworski, M
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Some advances in analytic hypoellipticity
Bruno Pini Mathematical Analysis Seminar, 2023 We present a brief survey on the theory of the real analytic regularity for the solutions to sums of squares of vector fields satisfying the Hörmander condition.
Marco Mughetti
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Analytic Hypoellipticity and the Treves Conjecture
Bruno Pini Mathematical Analysis Seminar, 2016 We are concerned with the problem of the analytic hypoellipticity; precisely, we focus on the real analytic regularity of the solutions of sums of squares with real analytic coefficients. Treves conjecture states that an operator of this type is analytic
Marco Mughetti
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Nonlinear eigenvalues and analytic hypoellipticity
Journal of Functional Analysis, 2004 22 pages, theorem 4.3 in new version is improved from m>18(old) to m>5(new) Proofs simplified considerably and typos ...
Ari Laptev +2 more
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Analytic and Gevrey hypoellipticity for perturbed sums of squares operators [PDF]
Annali Di Matematica Pura Ed Applicata, 2017 We prove a couple of results concerning pseudodifferential perturbations of differential operators being sums of squares of vector fields and satisfying Hörmander's condition. The first is on the minimal Gevrey regularity: if a sum of squares with analytic coefficients is perturbed with a pseudodifferential operator of order strictly less than its ...
Antonio Bove +2 more
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Global analytic hypoellipticity in the presence of symmetry [PDF]
Mathematical Research Letters, 1994 This paper deals with global analytic hypoellipticity for several classes of linear partial differential operators on some real analytic manifold without boundary. Assuming the operators to be \(C^\infty\) hypoelliptic and to commute with the action of a compact, connected Lie group the author proves a result on global analytic hypoellipticity.
Michael Christ, Christ Michael
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Analytic hypoellipticity for sums of squares and the Treves conjecture, II [PDF]
Analysis and PDE, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Antonio Bove +2 more
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Analytic hypoellipticity in the presence of nonsymplectic characteristic points
Journal of Functional Analysis, 2006 This paper deals with analytic hypoellipticity in the sense of germs of several classes of linear partial differential equations. Recently, N. Hanges proved that the operator in \(\mathbb{R}^3\): \[ P=\partial^2_t+ t^2\Delta_x+ \partial^2_{\theta(x)},\;\partial_{\theta(x)}= x_1{\partial\over\partial x_2}- x_2{\partial\over\partial x_1}, \] is analytic ...
Antonio Bove +2 more
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On the regularity of the solutions and of analytic vectors for “sums of squares”
Bruno Pini Mathematical Analysis Seminar, 2023 We present a brief survey on some recent results concerning the local and global regularity of the solutions for some classes/models of sums of squares of vector fields with real-valued real analytic coefficients of H"ormander type.
Gregorio Chinni
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(Semi-)global analytic hypoellipticity for a class of “sums of squares” which fail to be locally analytic hypoelliptic [PDF]
Proceedings of the American Mathematical Society, 2022 The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced by P. Albano, A. Bove, and M. Mughetti, satisfying the Hörmander condition and which fail to be either locally or microlocally analytic hypoelliptic.
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