Zobrazeno 1 - 10
of 225
pro vyhledávání: '"Weinkove, Ben"'
Autor:
Chau, Albert, Weinkove, Ben
The $p$-Laplacian evolution equation and the $\alpha$-Gauss curvature flow with a flat side are degenerate parabolic equations with evolving free boundaries. We give proofs of smooth short-time existence, up to the free boundaries, using a result of
Externí odkaz:
http://arxiv.org/abs/2412.10144
Autor:
Weinkove, Ben
Dimension reduction, widely used in science, maps high-dimensional data into low-dimensional space. We investigate a basic mathematical model underlying the techniques of stochastic neighborhood embedding (SNE) and its popular variant t-SNE. Distance
Externí odkaz:
http://arxiv.org/abs/2409.16963
Autor:
Chau, Albert, Weinkove, Ben
We prove existence of smooth solutions to linear degenerate parabolic equations on bounded domains assuming a structure condition of Fichera. We use this to give a proof of a smooth short time existence result for the porous medium equation $u_t = \D
Externí odkaz:
http://arxiv.org/abs/2311.14522
Autor:
Sherman, Morgan, Weinkove, Ben
Publikováno v:
J. Math. Anal. Appl. 527 (2023), no. 2, Paper No. 127469, 18 pp
The perfect conductivity problem concerns optimal bounds for the magnitude of an electric field in the presence of almost touching perfect conductors. This reduces to obtaining gradient estimates for harmonic functions with Dirichlet boundary conditi
Externí odkaz:
http://arxiv.org/abs/2301.03682
Autor:
Chau, Albert, Weinkove, Ben
Publikováno v:
Interfaces Free Bound. 25 (2023), no. 3, 517--523
We consider a well-known quasi-static model for the shape of a liquid droplet. The solution can be described in terms of time-evolving domains in $\mathbb{R}^n$. We give an example to show that convexity of the domain can be instantaneously broken.
Externí odkaz:
http://arxiv.org/abs/2210.12281
Autor:
Chau, Albert, Weinkove, Ben
Publikováno v:
Bull. Lond. Math. Soc. 55 (2023), no. 2, 706-716
We consider the Dirichlet problem for a class of semilinear equations on two dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmod
Externí odkaz:
http://arxiv.org/abs/2204.02384
Autor:
Tosatti, Valentino, Weinkove, Ben
Publikováno v:
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 33 (2022), no.1, 73-107
We give a survey on the Chern-Ricci flow, a parabolic flow of Hermitian metrics on complex manifolds. We emphasize open problems and new directions.
Comment: 30 pages; final version to appear in Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl
Comment: 30 pages; final version to appear in Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl
Externí odkaz:
http://arxiv.org/abs/2107.12928
Autor:
Weinkove, Ben
Publikováno v:
Math. Ann. 385 (2023), no. 1-2, 1-16
We consider the insulated conductivity problem with two unit balls as insulating inclusions, a distance of order $\varepsilon$ apart. The solution $u$ represents the electric potential. In dimensions $n \ge 3$ it is an open problem to find the optima
Externí odkaz:
http://arxiv.org/abs/2103.14143
Autor:
Chau, Albert, Weinkove, Ben
We show that the porous medium equation does not in general preserve $\alpha$-concavity of the pressure for $0\le\alpha<1/2$ or $1/2<\alpha\le 1$. In particular, this resolves an open problem of V\'azquez on whether concavity of pressure is preserved
Externí odkaz:
http://arxiv.org/abs/2011.03063