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Analytical Properties for Degenerate Equations

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Author(s)
Colding, Tobias Holck
•
Minicozzi II, William P.
Date Issued
2020
Publisher
Springer International Publishing
Citation
Colding, Tobias Holck and Minicozzi II, William P. 2020. "Analytical Properties for Degenerate Equations." 333.
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Author's final manuscript
Abstract
© 2020, Springer Nature Switzerland AG. By a classical result, solutions of analytic elliptic PDEs, like the Laplace equation, are analytic. In many instances, the properties that come from being analytic are more important than analyticity itself. Many important equations are degenerate elliptic and solutions have much lower regularity. Still, one may hope that solutions share properties of analytic functions. These properties are closely connected to important open problems. In this survey, we will explain why solutions of an important degenerate elliptic equation have analytic properties even though the solutions are not even C3.
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DOI of Published Version
10.1007/978-3-030-34953-0_4
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