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On the continuation by zero in Sobolev spaces with a small parameter

Article type: Research Article

Authors: Frank, L.S. | Heijstek, J.J.

Affiliations: Mathematisch Instituut, Katholieke Universiteit Nijmegen, 6525 ED Nijmegen, The Netherlands

Abstract: It is shown that the continuation by zero for families of Sobolev type spaces H(s),ε of vectorial order s=(s1,s2,s3) is a continuous linear mapping uniformly with respect to the parameter ε∈(0,1], provided that |s2|<½,|s2+s3|<½ and the boundary ∂U of the open set U where the functions are defined is a C∞-manifold. This result is needed in the theory of pseudodifferential coercive (elliptic) singular perturbations.

DOI: 10.3233/ASY-1988-1105

Journal: Asymptotic Analysis, vol. 1, no. 1, pp. 51-60, 1988

Received June 1987
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Published: 1988
Price: EUR 27.50
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