On a stationary transport equation

Summary 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].