Interpolation between subspaces of Hilbert spaces and applications to shift theorems for elliptic boundary value problems and finite element methods /
In the real method of interpolation one starts with two Hilbert spaces, X and Y, with certain properties and constructs a family of Hilbert spaces called the interpolation spaces. In applications to partial differential equations and finite element methods, the following question often arises: If t...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
2000.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=727852771&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | In the real method of interpolation one starts with two Hilbert spaces, X and Y, with certain properties and constructs a family of Hilbert spaces called the interpolation spaces. In applications to partial differential equations and finite element methods, the following question often arises: If the interpolation spaces X and Y are known Sobolev spaces, and if X[M] and Y[N] are closed subspaces of X and Y, respectively, what are the interpolation spaces of X[M] and Y[N] ? For certain boundary value problems, the answer to this kind of question, together with a complete characterization of the range of the corresponding differential operator, leads to stability estimates for solutions in terms of fractional norms. These types of estimates are known as shift theorems. The thesis is concerned with developing new interpolation results and shift theorems for the special case of polygonal plane domains, and presents some applications of the new results. |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | ix, 106 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilm Inc. |
| Bibliography: | Includes bibliographical references (leaves 102-105). |