Annali dell’Università di Ferrara

, Volume 32, Issue 1, pp 79–91 | Cite as

On a stationary transport equation

  • H. Beirão da Veiga


Let Ω, Γ,v, a andX be as described at the beginning of the introduction below, letp∈]1, +∞[, and setq=p/(p-1). Ifp>2, we also assume that the mean curvature {itx}{su(itx)} of Γ is everywhere nonnegative. In this paper we solve the existence problem in spacesX, for equation (1.1) below, ifX=W 0 1,q , orX=W −1,p. As a by-product, the solvability of (1.1) in spacesW 1,pandL pfollows (without any assumption on {itx}{su(itx)}). For more general results on the above problem, see ref. [1].


Banach Space Weak Solution Existence Problem Local Boundary Condition Suitable Positive Constant 
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  1. [1]
    H. Beirão da Veiga,Existence results in Sobolev spaces for a stationary transport equation, to appear.Google Scholar
  2. [2]
    H. Beirão da Veiga,An L p-theory for the n-dimensional, stationary, compressible, Navier-Stokes equations, and the incompressible limit for compressible fluids. The equilibrium solutions, to appear in Comm. Math. Physics (1987).Google Scholar
  3. [3]
    G. Fichera, Sulle equazioni differenziali lineari ellittico-paraboliche del secondo ordine, Atti Accad. Naz. Lincei, Mem. Cl. Sc. Fis. Mat. Nat., Sez. I,5 (1956), pp. 1–30.MathSciNetGoogle Scholar
  4. [4]
    G. Fichera,On an unified theory of boundary value problems for elliptic-parabolic equations of second order, in Boundary Problems. Differential Equations, Univ. of Wisconsin Press, Madison, Wisconsin (1960), pp. 97–120.Google Scholar
  5. [5]
    K. O. Friedrichs,Symmetric positive linear differential equations,Comm. Pure Appl. Math.,11 (1958), pp. 333–418.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    J. J. KohnL. Nirenberg,Degenerate elliptic-parabolic equations of second order, Comm. Pure Appl. Math.,20 (1967), pp. 797–872.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    P. D. LaxR. S. Phillips,Local boundary conditions for dissipative symmetric linear differential operators, Comm. Pure Appl. Math.,13 (1960), pp. 427–455.MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    S. Mizohata,The Theory of Partial Differential Equations, Cambridge Univ. Press, 1973.Google Scholar
  9. [9]
    O. A. Oleînik,A problem of Fichera (english translation), Soviet. Math. Dokl.,5 (1964), pp. 1129–1133.Google Scholar
  10. [10]
    O. A. Oleînik,Linear equations of second order with nonnegative characteristic form (english translation). Amer. Math. Soc. Transl., (2),65 (1967), pp. 167–199.Google Scholar
  11. [11]
    O. A. OleînikE. V. Radkevič,Second order equations with nonnegative characteristic form (english translation), Amer. Math. Soc., and Plenum Press, New York, 1973.Google Scholar

Copyright information

© Università degli Studi di Ferrara 1986

Authors and Affiliations

  • H. Beirão da Veiga
    • 1
  1. 1.Department of MathematicsUniversity of TrentoPovo (Trento)Italy

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