Open Access

Some elementary inequalities in gas dynamics equation

Journal of Inequalities and Applications20062006:21693

DOI: 10.1155/JIA/2006/21693

Received: 12 January 2005

Accepted: 25 August 2005

Published: 3 May 2006


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.


Authors’ Affiliations

Department of Mathematics, Volgograd State University


  1. Alessandrini G, Nesi V: Univalent-harmonic mappings. Archive for Rational Mechanics and Analysis 2001, 158: 155–171. 10.1007/PL00004242MATHMathSciNetView ArticleGoogle 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.MATHMathSciNetGoogle 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.MATHMathSciNetGoogle Scholar
  6. Hwang JF: A uniqueness theorem for the minimal surface equation. Pacific Journal of Mathematics 1996,176(2):357–364.MATHMathSciNetView ArticleGoogle 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, 251–271MathSciNetGoogle 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.2002.206.195MATHMathSciNetView ArticleGoogle Scholar


© Klyachin et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.