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Solutions of fixed sign of higher-order inhomogeneous equations of mixed elliptic-hyperbolic type

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Abstract

For a higher-order inhomogeneous equation of mixed elliptic-hyperbolic type, the property of the solution to be of fixed sign is established, depending on the sign of the right-hand side.

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References

  1. A. V. Bitsadze, Selected Works (Nauka, Nalchik, 2012) [in Russian].

    Google Scholar 

  2. R. Ya. Agishev, “On the problem of equations of mixed type,” Trudy Kazansk. Aviats. Inst. 35 (3), 3–10 (1957).

    Google Scholar 

  3. V. I. Zhegalov, “A boundary-value problem for a fourth-order equation of mixed type,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 4, 73–78 (1960).

    MathSciNet  Google Scholar 

  4. V. I. Zhegalov, “Boundary-value problem for amixed-type equation of higher order,” Dokl. Akad. Nauk SSSR 136 (2), 274–276 (1961) [Soviet Math. Dokl. 2, 45–47 (1961)].

    Google Scholar 

  5. S. Agmon, “Maximum theorems for solutions of higher-order elliptic equations,” Bull. Amer. Math. Soc. 66, 77–80 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  6. V. G. Maz’ya and B. A. Plamenevskii, “Abschätzungen im L p und in Hölderschen Klassen und das Miranda–Agmonsche Maximumprinzip für die Lösungen elliptischer Randwertprobleme in Gebieten mit singulären Punkten auf dem Rande,” Math. Nachr. 81, 25–82 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  7. V. G. Maz’ya and B. A. Plamenevskii, “On the maximum principle for the biharmonic equation in a domain with conical points,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 2, 52–59 (1981).

    MathSciNet  Google Scholar 

  8. J. Pipher and G. Verchota, “A maximum principle for biharmonic functions in Lipschitz and C1 domains,” Comment. Math. Helv. 68 (3), 385–414 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  9. J. Pipher and G. C. Verchota, “Maximum principles for the polyharmonic equation for Lipschitz domains,” Potential Anal. 4 (6), 615–636 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  10. A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Nauka, Moscow, 1966) [in Russian].

    MATH  Google Scholar 

  11. N. I. Muskhelishvili, Some Main Problems of the Mathematical Theory of Elasticity: Main Equations, Planar Theory of Elasticity, Twisting and Bending (Nauka, Moscow, 1966) [in Russian].

    MATH  Google Scholar 

  12. S. L. Sobolev, Introduction to the Theory of Cubature Formulas (Nauka, Moscow, 1974) [in Russian].

    Google Scholar 

  13. I. G. Petrovskii, Lectures in Partial Differential Equations (Gostekhizdat, Moscow–Leningrad, 1950) [in Russian].

    Google Scholar 

  14. K. B. Sabitov, Equations of Mathematical Physics (Fizmatlit, Moscow, 2013) [in Russian].

    Google Scholar 

  15. K. B. Sabitov, “Construction in explicit form of the solutions of the Darboux problem for the telegraph equation and their application to the treatment of integral equations. I,” Differ. Uravn. 26 (6), 1023–1032 (1990) [Differ. Equations 26 (6), 747–755 (1990)].

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute for Applied Studies, Sterlitamak, Russia

    K. B. Sabitov

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  1. K. B. Sabitov
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Correspondence to K. B. Sabitov.

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Original Russian Text © K. B. Sabitov, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 3, pp. 433–440.

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Sabitov, K.B. Solutions of fixed sign of higher-order inhomogeneous equations of mixed elliptic-hyperbolic type. Math Notes 100, 458–464 (2016). https://doi.org/10.1134/S0001434616090121

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  • DOI: https://doi.org/10.1134/S0001434616090121

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