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The Surface Diffusion And The Willmore Flow For Uniformly Regular Hypersurfaces, Jeremy Lecrone, Yuanzhen Shao, Gieri Simonett
The Surface Diffusion And The Willmore Flow For Uniformly Regular Hypersurfaces, Jeremy Lecrone, Yuanzhen Shao, Gieri Simonett
Department of Math & Statistics Faculty Publications
We consider the surface diffusion and Willmore flows acting on a general class of (possibly non–compact) hypersurfaces parameterized over a uniformly regular reference manifold possessing a tubular neighborhood with uniform radius. The surface diffusion and Willmore flows each give rise to a fourth–order quasilinear parabolic equation with nonlinear terms satisfying a specific singular structure. We establish well–posedness of both flows for initial surfaces that are C1+α–regular and parameterized over a uniformly regular hypersurface. For the Willmore flow, we also show long–term existence for initial surfaces which are C1+α–close to a sphere, and we prove …
A Template For Success: Celebrating The Work Of Judith Grabiner, Della Dumbaugh, Adrian Rice
A Template For Success: Celebrating The Work Of Judith Grabiner, Della Dumbaugh, Adrian Rice
Department of Math & Statistics Faculty Publications
Judith Grabiner is a mathematician who specializes in the history of mathematics. She is currently the Flora Sanborn Pitzer Professor Emerita of Mathematics at Pitzer College, one of the Claremont Colleges in Claremont, California. She has authored more than forty articles, as well as three books: The Origins of Cauchy’s Rigorous Calculus (1981), The Calculus as Algebra: J.-L. Lagrange, 1736–1813 (1990), and A Historian Looks Back: The Calculus as Algebra and Selected Writings (2010), which won the Beckenbach Prize from the Mathematical Association of America in 2014. She deliv- ered an invited address titled “The Centrality of Mathemat- ics in …
On Quasilinear Parabolic Equations And Continuous Maximal Regularity, Jeremy Lecrone, Gieri Simonett
On Quasilinear Parabolic Equations And Continuous Maximal Regularity, Jeremy Lecrone, Gieri Simonett
Department of Math & Statistics Faculty Publications
We consider a class of abstract quasilinear parabolic problems with lower–order terms exhibiting a prescribed singular structure. We prove well–posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global existence of solutions and we extend the generalized principle of linearized stability to settings with initial values in critical spaces. These general results are applied to the surface diffusion flow in various settings.