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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

Existence Theorem Null Space Adjoint Operator Finite Subset Fredholm Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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