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Analysis of the Finite Element Method for the Laplace–Beltrami Equation on Surfaces with Regions of High Curvature Using Graded Meshes
(Springer New York LLC, 2017)
We derive error estimates for the piecewise linear finite element approximation of the Laplace–Beltrami operator on a bounded, orientable, (Formula presented.), surface without boundary on general shape regular meshes. As ...
Evolution of an extremum by curvature motion
(Academic Press Inc., 2004)
In this paper we consider the evolution of an isolated extremum of a function under the curvature motion in the plane. We define different notions of circular extrema and show that, immediately after the motion begins, the ...
Existence of a BV solution for a mean curvature equation
(2021-10-25)
We prove the existence of a bounded variation solution for a quasilinear elliptic problem involving the mean curvature operator and a sublinear nonlinearity. We obtain such a solution as the limit of the solutions of another ...
MULTIPLE SOLUTIONS FOR THE MEAN CURVATURE EQUATION
(Juliusz Schauder Ctr Nonlinear StudiesTorunPolónia, 2010)
A numerical scheme for the curvature equation near the singularities
(2005)
In this paper we propose a modification in the usual numerical method for computing the solutions of the curvature equation in the plane . This modification takes place near the singularities of the image. We propose to ...
Multiple solutions for the mean curvature equation
(JULIUSZ SCHAUDER CTR NONLINEAR STUDIES, 2010)
Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the Three-Sphere
(2023)
In this article, we study eternal solutions to the Allen-Cahn equation in the 3-sphere, in view of the connection between the gradient flow of the associated energy functional, and the mean curvature flow. We construct ...
Interface dynamics in semilinear wave equations
(Springer, 2020)
We consider the wave equation epsilon(2)(-partial derivative(2)(t) + Delta)u + f(u) = 0 for 0 < epsilon << 1, where f is the derivative of a balanced, double-well potential, the model case being f(u) = u - u(3). For equations ...
The Mean Curvature Equation With Oscillating Nonlinearity
(Advanced Nonlinear Studies, 2015)