Theory of parabolic differential equations and its applications to geometric analysis
The main objective of this work is to establish a Holder and Lp theory for elliptic operators on manifolds with singularities. These operators may exhibit degenerate or singular behaviors while approaching the singular ends of the manifolds. Then we apply the theory established herein to several par...
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ndltd-VANDERBILT-oai-VANDERBILTETD-etd-06152015-1508122015-06-17T04:53:48Z Theory of parabolic differential equations and its applications to geometric analysis Shao, Yuanzhen Mathematics The main objective of this work is to establish a Holder and Lp theory for elliptic operators on manifolds with singularities. These operators may exhibit degenerate or singular behaviors while approaching the singular ends of the manifolds. Then we apply the theory established herein to several parabolic equations arising in geometric analysis, degenerate boundary value problems, and boundary blow-up problems. Larry L. Schumaker Zhaohua Ding Alexander M. Powell Emmanuele Dibenedetto Gieri Simonett VANDERBILT 2015-06-16 text application/pdf http://etd.library.vanderbilt.edu/available/etd-06152015-150812/ http://etd.library.vanderbilt.edu/available/etd-06152015-150812/ en restrictsix I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Vanderbilt University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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NDLTD |
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en |
| format |
Others
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| sources |
NDLTD |
| topic |
Mathematics |
| spellingShingle |
Mathematics Shao, Yuanzhen Theory of parabolic differential equations and its applications to geometric analysis |
| description |
The main objective of this work is to establish a Holder and Lp theory for elliptic operators on manifolds with singularities. These operators may exhibit degenerate or singular behaviors while approaching the singular ends of the manifolds. Then we apply the theory established herein to several parabolic equations arising in geometric analysis, degenerate boundary value problems, and boundary blow-up problems. |
| author2 |
Larry L. Schumaker |
| author_facet |
Larry L. Schumaker Shao, Yuanzhen |
| author |
Shao, Yuanzhen |
| author_sort |
Shao, Yuanzhen |
| title |
Theory of parabolic differential equations and its applications to geometric analysis |
| title_short |
Theory of parabolic differential equations and its applications to geometric analysis |
| title_full |
Theory of parabolic differential equations and its applications to geometric analysis |
| title_fullStr |
Theory of parabolic differential equations and its applications to geometric analysis |
| title_full_unstemmed |
Theory of parabolic differential equations and its applications to geometric analysis |
| title_sort |
theory of parabolic differential equations and its applications to geometric analysis |
| publisher |
VANDERBILT |
| publishDate |
2015 |
| url |
http://etd.library.vanderbilt.edu/available/etd-06152015-150812/ |
| work_keys_str_mv |
AT shaoyuanzhen theoryofparabolicdifferentialequationsanditsapplicationstogeometricanalysis |
| _version_ |
1716806000581804032 |