A priori estimate for a singularly perturbed mixed order boundary value problem
R. Denk and L. Volevich
Abstract. In this paper we study mixed-order (Douglis-Nirenberg) boundary value problems which depend on a real parameter but which are not elliptic with parameter in the sense of Agmon-Agranovich-Vishik. Using the method of the Newton polygon, we are able to prove a priori estimates for the solutions of such problems in corresponding Sobolev spaces. For the related singularly perturbed problem the boundary layer structure of the solutions is described. As an application of the a priori estimate, we obtain new estimates for a transmission problem studied by Faierman.
Russian J. Math. Phys. 7 (2000), 288-318.
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