Parabolic Mixed Problems with an Oblique Derivative

Abstract

where A is a second order elliptic differential operator on Ω and v is a real nonvanishing C∞ vector field defined in a neighborhood of Γ. When the problem is of non-degenerate type, that is, v is not tangent to Γ, various results have been obtained. Agranovich and Vishik [1] investigated mixed parabolic problems of general non-degenerate type. In the present paper we shall study the problem (0.1) in the case where v is tangent to Γ on its C∞ submanifold Γ0 (dim Γ0=dim Γ-1). Many authors have examined elliptic boundary value problems with the same oblique derivative (cf.