Monotonicity and its analytic and geometric implications
In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of function spaces and the geometry of the underlining spaces are intertwined. After briefly discussing some of the well-known analytical applications of monotonicit...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
National Academy of Sciences (U.S.)
2013
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| Online Access: | http://hdl.handle.net/1721.1/77236 https://orcid.org/0000-0001-6208-384X https://orcid.org/0000-0003-4211-6354 |
| Summary: | In this expository article, we discuss various monotonicity formulas for parabolic and elliptic operators and explain how the analysis of function spaces and the geometry of the underlining spaces are intertwined. After briefly discussing some of the well-known analytical applications of monotonicity for parabolic operators, we turn to their elliptic counterparts, their geometric meaning, and some geometric consequences. |
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