Proof of Theorem 1.1

  • Kazuaki Taira
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

In this chapter we consider the boundary value problem
$$\left\{ {\begin{array}{*{20}{c}} {Au = f{\text{ in D,}}} \\ {{L_0}u = \mu (x')\frac{{\partial u}}{{\partial n}} + \gamma (x')u = \varphi {\text{ on }}\partial {\text{D}}} \end{array}} \right.$$
(1.1)
in the framework of Sobolev spaces of L P style, and prove Theorem 1.1. If 1 < p < ∞ and s > 1+1/p, then we associate with problem (1.1) a continuous linear operator
$$A = (A,{L_0}):{H^{s,p}}(D) \to {H^{s - 2,p}}(D) \oplus B_{{L_0}}^{s - 1 - 1/p,p}(\partial D)$$
.

Keywords

Manifold 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Kazuaki Taira
    • 1
  1. 1.Institute of MathematicsUniversity of TsukubaTsukuba, IbarakiJapan

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