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Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients

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Authors:Günther Hörmann, Michael Oberguggenberger and Stevan Pilipovic
Journal:Trans. Amer. Math. Soc. 358 (2006), 3363-3383
MSC (2000):Primary 46F30, 35D10
DOI:https://doi.org/10.1090/S0002-9947-05-03759-1
Published electronically:May 9, 2005
MathSciNet review:2218979
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Abstract |References |Similar Articles |Additional Information

Abstract: We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth hypoelliptic symbols. Methodological novelties and technical refinements appear embedded into classical strategies of proof in order to cope with most delicate interferences by non-smooth lower order terms. We include simplified conditions which are applicable in special cases of interest.

  • 1.Jean-FrançoisColombeau, New generalized functions and multiplication ofdistributions, North-Holland Mathematics Studies, vol. 84,North-Holland Publishing Co., Amsterdam, 1984. Notas de Matemática[Mathematical Notes], 90. MR738781
  • 2.Jean-FrançoisColombeau, Elementary introduction to new generalizedfunctions, North-Holland Mathematics Studies, vol. 113,North-Holland Publishing Co., Amsterdam, 1985. Notes on Pure Mathematics,103. MR808961
  • 3.N.Dapić, S.Pilipović, and D.Scarpalézos, Microlocal analysis of Colombeau’sgeneralized functions: propagation of singularities, J. Anal. Math.75 (1998), 51–66. MR1655823, https://doi.org/10.1007/BF02788691
  • 4.ClaudiaGaretto, Pseudo-differential operators in algebras of generalizedfunctions and global hypoellipticity, Acta Appl. Math.80 (2004), no. 2, 123–174. MR2035505, https://doi.org/10.1023/B:ACAP.0000013814.89972.3c
  • 5.MichaelGrosser, MichaelKunzinger, MichaelOberguggenberger, and RolandSteinbauer, Geometric theory of generalized functions withapplications to general relativity, Mathematics and its Applications,vol. 537, Kluwer Academic Publishers, Dordrecht, 2001. MR1883263
  • 6.LarsHörmander, Fourier integral operators. I, Acta Math.127 (1971), no. 1-2, 79–183. MR388463, https://doi.org/10.1007/BF02392052
  • 7.LarsHörmander (ed.), Seminar on Singularities of Solutions ofLinear Partial Differential Equations, Annals of Mathematics Studies,vol. 91, Princeton University Press, Princeton, N.J.; University ofTokyo Press, Tokyo, 1979. Held at the Institute for Advanced Study,Princeton, N.J., 1977/78. MR547013
  • 8.LarsHörmander, The analysis of linear partial differentialoperators. I, Grundlehren der Mathematischen Wissenschaften[Fundamental Principles of Mathematical Sciences], vol. 256,Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR717035
    LarsHörmander, The analysis of linear partial differentialoperators. II, Grundlehren der Mathematischen Wissenschaften[Fundamental Principles of Mathematical Sciences], vol. 257,Springer-Verlag, Berlin, 1983. Differential operators with constantcoefficients. MR705278
    LarsHörmander, The analysis of linear partial differentialoperators. III, Grundlehren der Mathematischen Wissenschaften[Fundamental Principles of Mathematical Sciences], vol. 274,Springer-Verlag, Berlin, 1985. Pseudodifferential operators. MR781536
  • 9.GüntherHörmann, Integration and microlocal analysis in Colombeaualgebras of generalized functions, J. Math. Anal. Appl.239 (1999), no. 2, 332–348. MR1723064, https://doi.org/10.1006/jmaa.1999.6565
  • 10.G.Hörmann and MaartenV. de Hoop, Microlocal analysis and global solutions of somehyperbolic equations with discontinuous coefficients, Acta Appl. Math.67 (2001), no. 2, 173–224. MR1848743, https://doi.org/10.1023/A:1010614332739
  • 11.GüntherHörmann and MichaelKunzinger, Microlocal properties of basic operations in Colombeaualgebras, J. Math. Anal. Appl. 261 (2001),no. 1, 254–270. MR1850971, https://doi.org/10.1006/jmaa.2001.7498
  • 12.GüntherHörmann and MichaelOberguggenberger, Elliptic regularity and solvability for partialdifferential equations with Colombeau coefficients, Electron. J.Differential Equations (2004), No. 14, 30. MR2036198
  • 13.HikosaburoKomatsu, Microlocal analysis in Gevrey classes and in complexdomains, Microlocal analysis and applications (Montecatini Terme,1989) Lecture Notes in Math., vol. 1495, Springer, Berlin, 1991,pp. 161–236. MR1178558, https://doi.org/10.1007/BFb0085124
  • 14.MariaMascarello and LuigiRodino, Partial differential equations with multiplecharacteristics, Mathematical Topics, vol. 13, Akademie Verlag,Berlin, 1997. MR1608649
  • 15.M.Nedeljkov, S.Pilipović, and D.Scarpalézos, The linear theory of Colombeau generalizedfunctions, Pitman Research Notes in Mathematics Series, vol. 385,Longman, Harlow, 1998. MR1638310
  • 16.MichaelOberguggenberger, Hyperbolic systems with discontinuouscoefficients: generalized solutions and a transmission problem inacoustics, J. Math. Anal. Appl. 142 (1989),no. 2, 452–467. MR1014590, https://doi.org/10.1016/0022-247X(89)90014-0
  • 17.M.Oberguggenberger, Multiplication of distributions and applicationsto partial differential equations, Pitman Research Notes inMathematics Series, vol. 259, Longman Scientific & Technical,Harlow; copublished in the United States with John Wiley & Sons, Inc.,New York, 1992. MR1187755
  • 18.CesareParenti and LuigiRodino, Examples of hypoelliptic operators which are notmicrohypoelliptic, Boll. Un. Mat. Ital. B (5) 17(1980), no. 1, 390–409 (English, with Italian summary). MR572609
  • 19.LuigiRodino, Linear partial differential operators in Gevreyspaces, World Scientific Publishing Co., Inc., River Edge, NJ, 1993.MR1249275
  • 20.ElemerE. Rosinger, Nonlinear partial differential equations,North-Holland Mathematics Studies, vol. 164, North-Holland PublishingCo., Amsterdam, 1990. An algebraic view of generalized solutions. MR1091547
  • 21.MikioSato, TakahiroKawai, and MasakiKashiwara, Microfunctions and pseudo-differential equations,Hyperfunctions and pseudo-differential equations (Proc. Conf., Katata,1971; dedicated to the memory of André Martineau), Springer,Berlin, 1973, pp. 265–529. Lecture Notes in Math., Vol. 287. MR0420735
  • 22.LaurentSchwartz, Sur l’impossibilité de la multiplication desdistributions, C. R. Acad. Sci. Paris 239 (1954),847–848 (French). MR64324
  • 23.MichaelE. Taylor, Pseudodifferential operators, PrincetonMathematical Series, vol. 34, Princeton University Press, Princeton,N.J., 1981. MR618463
  • 24.H.Triebel, Interpolation theory, function spaces, differentialoperators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978. MR500580
Jour. d'Analyse Math., 75:51-66, 1998. MR 1655823
4.
C. Garetto.
Pseudo-differential operators in algebras of generalized functions and global hypoellipticity.
Acta Applicandae Mathematicae, 80:123-174, 2004. MR 2035505
5.
M. Grosser, M. Kunzinger, M. Oberguggenberger, and R. Steinbauer.
Geometric theory of generalized functions.
Kluwer, Dordrecht, 2001. MR 1883263
6.
L. Hörmander.
Fourier integral operators I.
Acta Math., 127:79-183, 1971. MR 0388463
7.
L. Hörmander, editor.
Seminar on singularities of solutions of linear partial differential equations, Annals of Mathematics Studies 91, Princeton, New Jersey, 1979. Princeton University Press and University of Tokyo Press. MR 0547013
8.
L. Hörmander.
The analysis of linear partial differential operators, volume I-IV.
Springer-Verlag, 83 1983-85, 2nd Ed. Vol. I 1990. MR 0717035; MR 0705278 (85g:35002b); MR 0781536; MR 0781536 (87d:35002b)
9.
G. Hörmann.
Integration and microlocal analysis in Colombeau algebras.
J. Math. Anal. Appl., 239:332-348, 1999. MR 1723064
10.
G. Hörmann and M. V. de Hoop.
Microlocal analysis and global solutions of some hyperbolic equations with discontinuous coefficients.
Acta Appl. Math., 67:173-224, 2001. MR 1848743
11.
G. Hörmann and M. Kunzinger.
Microlocal analysis of basic operations in Colombeau algebras.
J. Math. Anal. Appl., 261:254-270, 2001. MR 1850971
12.
G. Hörmann and M. Oberguggenberger.
Elliptic regularity and solvability for partial differential equations with Colombeau coefficients.
Electron. J. Diff. Eqns., 2004(14):1-30, 2004. MR 2036198
13.
H. Komatsu.
Microlocal analysis in Gevrey classes and in convex domains.
In J. M. Bony and L. Cattabriga, editors, Microlocal analysis and applications, Lecture Notes in Mathematics 1495, pages 161-236. Springer-Verlag, Berlin, 1991. MR 1178558
14.
M. Mascarello and L. Rodino.
Partial differential equations with multiple characteristics.
Akademie Verlag, Berlin, 1997. MR 1608649
15.
M. Nedeljkov, S. Pilipovic, and D. Scarpalézos.
The linear theory of Colombeau generalized functions.
Longman, Harlow, 1998. MR 1638310
16.
M. Oberguggenberger.
Hyperbolic systems with discontinuous coefficients: generalized solutions and a transmission problem in acoustics.
J. Math. Anal. Appl., 142:452-467, 1989. MR 1014590
17.
M. Oberguggenberger.
Multiplication of distributions and applications to partial differential equations.
Longman Scientific & Technical, 1992. MR 1187755
18.
C. Parenti and L. Rodino.
Examples of hypoelliptic operators which are not microhypoelliptic.
Bolletino U.M.I., 17-B:390-409, 1980. MR 0572609
19.
L. Rodino.
Linear partial differential operators in Gevrey spaces.
World Scientific, Singapore, 1993. MR 1249275
20.
E. E. Rosinger.
Non-linear partial differential equations. An algebraic view of generalized solutions.
North-Holland, Amsterdam, 1990. MR 1091547
21.
M. Sato, T. Kawai, and M. Kashiwara.
Microfunctions and pseudo differential equations.
In H. Komatsu, editor, Hyperfunctions and pseudodifferential equations, Lecture Notes in Mathematics 287, pages 265-529. Springer-Verlag, New York, 1973. MR 0420735
22.
L. Schwartz.
Sur l'impossibilité de la multiplication des distributions.
C. R. Acad. Sci. Paris, 239:847-848, 1954. MR 0064324
23.
M. E. Taylor.
Pseudodifferential operators.
Princeton University Press, Princeton, New Jersey, 1981. MR 0618463
24.
H. Triebel.
Interpolation theory, function spaces, differential operators.
North-Holland Mathematical Library Vol. 18. North-Holland, Amsterdam, 1978.MR 0500580
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Additional Information
Günther Hörmann
Affiliation:Institut für Mathematik, Universität Wien, A-1010 Vienna, Austria
Michael Oberguggenberger
Affiliation:Institut für Technische Mathematik, Geometrie und Bauinformatik, Universität Innsbruck, Technikerstrasse 13, A-6020 Innsbruck, Austria
Stevan Pilipovic
Affiliation:Institute of Mathematics and Informatics, Faculty of Science and Mathematics, University of Novi Sad, 21000 Novi Sad, Serbia
DOI:https://doi.org/10.1090/S0002-9947-05-03759-1
Keywords:Partial differential operators with non-smooth coefficients,generalized (micro-) hypoellipticity,microlocal regularity,algebras of generalized functions
Received by editor(s):March 24, 2003
Received by editor(s) in revised form:May 4, 2004
Published electronically:May 9, 2005
Additional Notes:The first author was supported by FWF grant P14576-MAT
The third author was supported by the MNTR of Serbia, Project 1835
Article copyright:© Copyright 2005American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.





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