Relevant bibliographies by topics / Hypoellipticity

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Hypoellipticity'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 May 2024

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Journal articles on the topic "Hypoellipticity"

1

Himonas, A. Alexandrou. "analytic hypoellipticity." Duke Mathematical Journal 59, no. 1 (1989): 265–87. http://dx.doi.org/10.1215/s0012-7094-89-05909-7.

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Donno, Giuseppe De. "Generalized Vandermonde determinants for reversing Taylor's formula and application to hypoellipticity." Tamkang Journal of Mathematics 38, no. 2 (2007): 183–89. http://dx.doi.org/10.5556/j.tkjm.38.2007.89.

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The problem of the hypoellipticity of the linear partial differential operators with constant coefficients was completely solved by H"{o}r-man-der in [5]. He listed many equivalent algebraic conditions on the polynomial symbol of the operator, each necessary and sufficient for hypoellipticity. In this paper we employ two Mitchell's Theorems (1881) regarding a type of Generalized Vandermonde Determinants, for inverting Taylor's formula of polynomials in several variables with complex coefficients. We obtain then a more direct and easy proof of an
 equivalence for the mentioned H"{o}r-man-d
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Street, Brian. "What is ...Hypoellipticity?" Notices of the American Mathematical Society 65, no. 04 (2018): 1. http://dx.doi.org/10.1090/noti1670.

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Bergamasco, A. P., G. A. Mendoza, and S. Zani. "On Global Hypoellipticity." Communications in Partial Differential Equations 37, no. 9 (2012): 1517–27. http://dx.doi.org/10.1080/03605302.2011.641054.

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Bergamasco, Adalberto P., and Sérgio Luís Zani. "Global Hypoellipticity of a Class of Second Order Operators." Canadian Mathematical Bulletin 37, no. 3 (1994): 301–5. http://dx.doi.org/10.4153/cmb-1994-045-4.

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AbstractWe show that almost all perturbations P — λ, λ € C, of an arbitrary constant coefficient partial differential operator P are globally hypoelliptic on the torus. We also give a characterization of the values λ € C for which the operator is globally hypoelliptic; in particular, we show that the addition of a term of order zero may destroy the property of global hypoellipticity of operators of principal type, contrary to that happens with the usual (local) hypoellipticity.
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Nedeljkov, M., and S. Pilipović. "Hypoelliptic differential operators with generalized constant coefficients." Proceedings of the Edinburgh Mathematical Society 41, no. 1 (1998): 47–60. http://dx.doi.org/10.1017/s0013091500019428.

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The space of Colombeau generalized functions is used as a frame for the study of hypoellipticity of a family of differential operators whose coefficients depend on a small parameter ε.There are given necessary and sufficient conditions for the hypoellipticity of a family of differential operators with constant coefficients which depend on ε and behave like powers of ε as ε→0. The solutions of such family of equations should also satisfy the power order estimate with respect to ε.
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Nedeljkov, Marko, та Stevan Pilipovic. "On hypoellipticity in ς". Bulletin: Classe des sciences mathematiques et natturalles 123, № 27 (2002): 47–56. http://dx.doi.org/10.2298/bmat0227047n.

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We give a condition of sufficiency for the hypoellipticity of a family of equations with constant coefficients satisfied prescribed power growth rate with respect to ? ? (0, 1). The framework is Colombeau algebra of generalized functions.
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Street, Brian. "WHAT ELSE about...Hypoellipticity?" Notices of the American Mathematical Society 65, no. 04 (2018): 1. http://dx.doi.org/10.1090/noti1664.

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Cordaro, Paulo D., and Nicholas Hanges. "Hyperfunctions and (analytic) hypoellipticity." Mathematische Annalen 344, no. 2 (2008): 329–39. http://dx.doi.org/10.1007/s00208-008-0308-2.

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Yoshino, Masafumi. "Global hypoellipticity and continued fractions." Tsukuba Journal of Mathematics 15, no. 1 (1991): 193–203. http://dx.doi.org/10.21099/tkbjm/1496161581.

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Dissertations / Theses on the topic "Hypoellipticity"

1

Valentin, Jérôme. "Extensions de la formule d'Itô par le calcul de Malliavin et application à un problème variationnel." Thesis, Paris, ENST, 2012. http://www.theses.fr/2012ENST0029/document.

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Ce travail de thèse est consacré à l'extension de la formule d'Itô au cas de chemins à variations bornées à valeurs dans l'espace des distributions tempérées composés par des processus réguliers au sens de Malliavin. On s'attache en particulier à faire des hypothèses de régularité minimales, ce qui donne accès à un certain nombre d'applications de notre principal résultat, en particulier à l'étude d'un problème variationnel. Le premier chapitre est consacré à des rappels de calcul de Malliavin. Le deuxième donne des résultats sur la topologie sur la classe de Schwartz et l'espace des distribut
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2

Tartakoff, David S., and Andreas Cap@esi ac at. "Results in Gevrey and Analytic Hypoellipticity." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi967.ps.

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Wenyi, Chen, and Wang Tianbo. "The hypoellipticity of differential forms on closed manifolds." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2980/.

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In this paper we consider the hypo-ellipticity of differential forms on a closed manifold.The main results show that there are some topological obstruct for the existence of the differential forms with hypoellipticity.
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Chen, Hua, Wei-Xi Li, and Chao-Jiang Xu. "Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations." Universität Potsdam, 2007. http://opus.kobv.de/ubp/volltexte/2009/3028/.

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Shimoda, Taishi. "Hypoellipticity of second order differential operators with sign-changing principal symbols /." Sendai : Tohoku Univ, 2000. http://www.loc.gov/catdir/toc/fy0713/2007329003.html.

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Pigato, Paolo. "Tube estimates for hypoelliptic diffusions and scaling properties of stochastic volatility models." Thesis, Paris Est, 2015. http://www.theses.fr/2015PESC1029/document.

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Dans cette thèse on aborde deux problèmes. Dans la première partie on considère des diffusions hypoelliptiques, à la fois sur une condition d'Hormander forte et faible. On trouve des estimations gaussiennes pour la densité de la loi de la solution à un temps court fixé. Un outil fondamental pour prouver ces estimations est le calcul de Malliavin, et en particulier on utilise des techniques développées récemment pour faire face à des problèmes de dégénérescence. Ensuite, grâce à ces estimations en temps court, on trouve des bornes inférieures et supérieures exponentielles sur la probabilité que
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7

Chinni, Gregorio <1980&gt. "Analytic and gevrey (micro-)hypoellipticity for sums of squares: an FBI approach." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2008. http://amsdottorato.unibo.it/947/1/Tesi_Chinni_Gregorio.pdf.

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Chinni, Gregorio <1980&gt. "Analytic and gevrey (micro-)hypoellipticity for sums of squares: an FBI approach." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2008. http://amsdottorato.unibo.it/947/.

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9

Valentin, Jérôme. "Extensions de la formule d'Itô par le calcul de Malliavin et application à un problème variationnel." Electronic Thesis or Diss., Paris, ENST, 2012. http://www.theses.fr/2012ENST0029.

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Ce travail de thèse est consacré à l'extension de la formule d'Itô au cas de chemins à variations bornées à valeurs dans l'espace des distributions tempérées composés par des processus réguliers au sens de Malliavin. On s'attache en particulier à faire des hypothèses de régularité minimales, ce qui donne accès à un certain nombre d'applications de notre principal résultat, en particulier à l'étude d'un problème variationnel. Le premier chapitre est consacré à des rappels de calcul de Malliavin. Le deuxième donne des résultats sur la topologie sur la classe de Schwartz et l'espace des distribut
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Pigato, Paolo. "Tube Estimates for Hypoelliptic Diffusions and Scaling Properties of Stochastic Volatility Models." Doctoral thesis, Università degli studi di Padova, 2015. http://hdl.handle.net/11577/3424189.

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In this thesis we address two problems. In the first part we consider hypoelliptic diffusions, under both strong and weak Hormander condition. We find Gaussian estimates for the density of the law of the solution at a fixed, short time. A main tool to prove these estimates is Malliavin Calculus, in particular some techniques recently developed to deal with degenerate problems. We then use these short-time estimates to show exponential two-sided bounds for the probability that the diffusion remains in a small tube around a deterministic path up to a given time. In our hypoelliptic framework, t
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Books on the topic "Hypoellipticity"

1

Boggiatto, Paolo. Global hypoellipticity and spectral theory. Akademie Verlag, 1996.

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Yu, Ching-Chau. Nonlinear eigenvalues and analytic-hypoellipticity. American Mathematical Society, 1998.

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Bell, Denis R. Degenerate stochastic differential equations and hypoellipticity. Longman, 1995.

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Bell, Denis R. Degenerate stochastic differential equations and hypoellipticity. Longman, 1995.

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5

Shimoda, Taishi. Hypoellipticity of second order differential operators with sign-changing principal symbols. Tohoku University, 2000.

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6

service), SpringerLink (Online, ed. Nonelliptic Partial Differential Equations: Analytic Hypoellipticity and the Courage to Localize High Powers of T. Springer Science+Business Media, LLC, 2011.

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Jean, Nourrigat, ed. Hypoellipticité maximale pour des opérateurs polynomes de champs de vecteurs. Birkhäuser, 1985.

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Rockland, C. Hypoellipticity and Eigenvalue Asymptotics. Springer London, Limited, 2006.

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9

Bell, Denis. Degenerate Stochastic Differential Equations and Hypoellipticity. Taylor & Francis Group, 1996.

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10

Street, Brian. The Calder´on-Zygmund Theory II: Maximal Hypoellipticity. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691162515.003.0002.

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This chapter remains in the single-parameter case and turns to the case when the metric is a Carnot–Carathéodory (or sub-Riemannian) metric. It defines a class of singular integral operators adapted to this metric. The chapter has two major themes. The first is a more general reprise of the trichotomy described in Chapter 1 (Theorem 2.0.29). The second theme is a generalization of the fact that Euclidean singular integral operators are closely related to elliptic partial differential equations. The chapter also introduces a quantitative version of the classical Frobenius theorem from different
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Book chapters on the topic "Hypoellipticity"

1

Gårding, Lars. "Hypoellipticity." In University Lecture Series. American Mathematical Society, 1997. http://dx.doi.org/10.1090/ulect/011/09.

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Christ, Michael. "Hypoellipticity: Geometrization and speculation." In Complex Analysis and Geometry. Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8436-5_5.

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Tartakoff, David S. "Gevrey and Analytic Hypoellipticity." In Microlocal Analysis and Spectral Theory. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5626-4_2.

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Malliavin, Paul. "Hypoellipticity in Infinite Dimensions." In Diffusion Processes and Related Problems in Analysis, Volume I. Birkhäuser Boston, 1990. http://dx.doi.org/10.1007/978-1-4684-0564-4_2.

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Cordaro, Paulo D., and Nicholas Hanges. "Symplectic strata and analytic hypoellipticity." In Phase Space Analysis of Partial Differential Equations. Birkhäuser Boston, 2006. http://dx.doi.org/10.1007/978-0-8176-4521-2_7.

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Helffer, Bernard, and Francis Nier. "7. Hypoellipticity and Nilpotent Groups." In Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/978-3-540-31553-7_7.

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Mendoza, Gerardo A. "Topological Implications of Global Hypoellipticity." In Microlocal Methods in Mathematical Physics and Global Analysis. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0466-0_29.

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Tartakoff, David S. "Nonsymplectic Strata and Germ Analytic Hypoellipticity." In Nonelliptic Partial Differential Equations. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9813-2_11.

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Christ, Michael. "REMARKS ON ANALYTIC HYPOELLIPTICITY OF ∂̅b." In Modern Methods in Complex Analysis (AM-137), edited by Thomas Bloom, David W. Catlin, John P. D'Angelo, and Yum-Tong Siu. Princeton University Press, 1996. http://dx.doi.org/10.1515/9781400882571-007.

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Wong, M. W. "Global Hypoellipticity in the Schwartz Space." In Partial Differential Equations, 2nd ed. Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003206781-10.

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Conference papers on the topic "Hypoellipticity"

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Hairer, Martin. "Hypoellipticity in infinite dimensions." In Proceedings of the 7th International ISAAC Congress. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814313179_0062.

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AYELE, TSEGAYE G., and WORKU T. BITEW. "PARTIAL HYPOELLIPTICITY OF DIFFERENTIAL OPERATORS." In Proceedings of the 6th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812837332_0056.

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Garetto, Claudia. "G- and G∞-hypoellipticity of partial differential operators with constant Colombeau coefficients." In Linear and Non-Linear Theory of Generalized Functions and its Applications. Institute of Mathematics Polish Academy of Sciences, 2010. http://dx.doi.org/10.4064/bc88-0-9.

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POPIVANOV, P. R. "ON THE HYPOELLIPTICITY OF SOME CLASSES OF OVERDETERMINED SYSTEMS OF DIFFERENTIAL AND PSEUDODIFFERENTIAL OPERATORS." In Proceedings of the 8th International Workshop on Complex Structures and Vector Fields. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812709806_0030.

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Reports on the topic "Hypoellipticity"

1

Ustunel, A. S. Hypoellipticity of the Stochastic Partial Differential Operators. Defense Technical Information Center, 1985. http://dx.doi.org/10.21236/ada170326.

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