PORTUGALIAE MATHEMATICA Vol. 54, No. 3, pp. 317333 (1997) 

About Steady Transport Equation II  Schauder Estimates in Domains with Smooth BoundariesAntonin NovotnyDepartment of Mathematics, ETMA,B.P. 132, 839 57 La Garde  FRANCE Abstract: This paper is a continuation of our work [7]. We investigate steady transport equation $$ \lambda\,z+w\cdot\nabla z+a\,z=f\nvirg \lambda>0, $$ in various domains (bounded or unbounded) with sufficiently smooth compact or noncompact boundaries. The coefficients $w$ and $a$ are ``sufficiently smooth functions, ``small in appropriate norms. There is no transport of $z$ through the boundary. Under these assumptions, we study existence, regularity, uniqueness and asymptotic behaviour (when the domain is unbounded) of solutions in spaces of Holder continuous functions. The corresponding estimates are derived. The results presented here have found a series of applications in the compressible fluid dynamics. Classification (MSC2000): 35Q35, 35L, 76N Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1997 Sociedade Portuguesa de Matemática
