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A Link between Local Solvability and Partial Analyticity of Several Classes of Degenerate Parabolic Operators

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Hyperbolic Problems and Regularity Questions

Part of the book series: Trends in Mathematics ((TM))

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Abstract

The aim of this work is to find a necessary and sufficient condition for local solvability of some classes of degenerate parabolic operators. The conditions are imposed on the right-hand side f of the corresponding equation. It is well known that the operators under consideration are nonsolvable for a “massive” set of smooth functions f.

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References

  1. So-Chin Chen and Mei-Chi Shaw, Partial differential equations in several complex variables. AMS/IP Studies in Advanced Mathematics 19, Providence, International Press, Boston, MA, 2001.

    Google Scholar 

  2. M. Cicognani and L. Zanghirati, On a class of unsolvable operators. Ann. Scuola Norm. Sup. Pisa, 20 (1993), 357–369.

    MathSciNet  Google Scholar 

  3. T. Gramchev and P. Popivanov, Partial differential equations. Approximate solutions in scales of functional spaces. Mathematical Research 108, Wiley-VCH, Berlin, 2000.

    Google Scholar 

  4. P. Greiner, J.J. Kohn and E. Stein, Necessary and sufficient conditions for solvability of the Lewy equation. Proc. Nat. Acad. Sci. USA 72 (1975) n. 9, 3287–3289.

    Article  MathSciNet  Google Scholar 

  5. L. Hörmander, Linear partial differential operators. Springer Verlag, Berlin, 1963.

    MATH  Google Scholar 

  6. Y. Kannai, An unsolvable hypoelliptic differential equation. Israel J. Math., 9 (1971), 306–315.

    MathSciNet  Google Scholar 

  7. N.V. Krylov, Lectures on elliptic and parabolic equations in Holder spaces. Graduate studies in Mathematics, 12, AMS, Providence, RI, 1996.

    Google Scholar 

  8. H. Lewy, An example of a smooth linear partial differential operator without solution. Ann. of Math. 66 (1957), 155–158.

    Article  MathSciNet  Google Scholar 

  9. M. Mascarello, L. Rodino, Partial Differential equations with multiple characteristics. Academie Verlag, Berlin, 1997.

    MATH  Google Scholar 

  10. D. Mumford, Tata lectures on theta I, II. Progress in Mathematics 28, 43, Birkhäuser, Boston, 1983, 1984.

    Google Scholar 

  11. H. Ninomiya, Necessary and sufficient conditions for local solvability of the Mizohata equations. J.Math. Kyoto Univ., 28 (1988), 593–603.

    MathSciNet  Google Scholar 

  12. J. Sjostrand, Operators of principal type with interior boundary conditions. Acta Math., 130 (1973), 1–51.

    Article  MathSciNet  Google Scholar 

  13. A. Samarskii and A. Tihonov, Equations of mathematical physics. (In Russian.) Nauka, Moscow, 1966.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematics and Informatics, Akad. G. Bonchev Str. bl. 8, 1113, Sofia, Bulgaria

    Petar R. Popivanov

Authors
  1. Petar R. Popivanov
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Editor information

Editors and Affiliations

  1. Dipartimento di Matematica, Università di Ferrara via Machiavelli, 35, I-44100, Ferrara, Italy

    Mariarosaria Padula  & Luisa Zanghirati  & 

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Popivanov, P.R. (2006). A Link between Local Solvability and Partial Analyticity of Several Classes of Degenerate Parabolic Operators. In: Padula, M., Zanghirati, L. (eds) Hyperbolic Problems and Regularity Questions. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7451-8_17

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