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Annali di Matematica Pura ed Applicata

, Volume 90, Issue 1, pp 99–147 | Cite as

Singularly perturbed elliptic boundary value problems

I. Poisson kernels and potential theory
  • Paul C. Fife
Article

Summary

The paper treats elliptic operators of the form L(ɛ∂1, ..., ɛ∂n), where L is a polynomial in a variables of order 2m1, and ɛ is a small parameter. Solutionsu ɛ of Lu=0 in a half space satisfyng conditions Bj(ɛ∂1, ɛ∂2, ..., ɛ∂n)u=ɛγjϕj(x)(j=1, ..., m1) on the boundary are constructed and estimated using Hölder norms, Poisson kernels, and an elaborate potential theory. Properties of the interior limit u0=u ɛ(κ) are studied. The paper is preparatory to a detailed investigation of Schauder estimates for such problems with variables coefficients.

Keywords

Small Parameter Variable Coefficient Half Space Potential Theory Elliptic 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

© Nicola Zanichelli Editore 1971

Authors and Affiliations

  • Paul C. Fife
    • 1
  1. 1.USA

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