Singularly perturbed elliptic boundary value problems
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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.
KeywordsSmall Parameter Variable Coefficient Half Space Potential Theory Elliptic Operator
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