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Some elementary inequalities in gas dynamics equation


We describe the sets on which difference of solutions of the gas dynamics equation satisfy some special conditions. By virtue of nonlinearity of the equation the sets depend on the solution gradient quantity. We show double-ended estimates of the given sets and some properties of these estimates.



  1. Alessandrini G, Nesi V: Univalent-harmonic mappings. Archive for Rational Mechanics and Analysis 2001, 158: 155–171. 10.1007/PL00004242

    Article  MATH  MathSciNet  Google Scholar 

  2. Bers L: Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Surveys in Applied Mathematics. Volume 3. John Wiley & Sons; New York; Chapman & Hall; London; 1958:164.

    Google Scholar 

  3. Collin P, Krust R: Le probléme de Dirichlet pour l'equation des surfaces minimales sur des domaines non bornés. Bulletin de la Société Mathématique de France 1991,119(4):443–458.

    MATH  MathSciNet  Google Scholar 

  4. Faraco D: Beltrami operators and microstructure, Academic dissertation. Department of Mathematics, Faculty of Science, University of Helsinki, Helsinki; 2002.

    Google Scholar 

  5. Hwang JF: Comparison principles and Liouville theorems for prescribed mean curvature equations in unbounded domains. Annali della Scuola Normale Superiore di Pisa 1988,15(3):341–355.

    MATH  MathSciNet  Google Scholar 

  6. Hwang JF: A uniqueness theorem for the minimal surface equation. Pacific Journal of Mathematics 1996,176(2):357–364.

    Article  MATH  MathSciNet  Google Scholar 

  7. Lavrentiev MA, Shabat BV: Problems of Hydrodynamics and Their Mathematical Models. Nauka, Moscow; 1973:416.

    Google Scholar 

  8. Miklyukov VM: On a new aproach to Bernshtein's theorem and related questions for equations of minimal surface type. Matematicheskiĭ Sbornik. Novaya Seriya 1979,108(150)(2):268–289, 304. English translation in Mathematics of the USSR Sbornik $36$ (1980), no. 2, 251–271 English translation in Mathematics of the USSR Sbornik $36$ (1980), no. 2, 251–271

    MathSciNet  Google Scholar 

  9. Pigola S, Rigoli M, Setti AG: Some remarks on the prescribed mean curvature equation on complete manifolds. Pacific Journal of Mathematics 2002,206(1):195–217. 10.2140/pjm.2002.206.195

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to V. A. Klyachin.

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Klyachin, V.A., Kochetov, A.V. & Miklyukov, V.M. Some elementary inequalities in gas dynamics equation. J Inequal Appl 2006, 21693 (2006).

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