A variational view at the time-dependent minimal surface equation
Journal of Evolution Equations, 2011 The authors proved a relaxation result that the minimizers of the weighted energy-dissipation functional converges to the gradient flow trajectories of the relaxed area functional. The result is then extended to general parabolic quasilinear equations arising as gradient flows of convex functionals with linear growth.
E. Spadaro, U. Stefanelli
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Plateau problem and minimal surfaces: numerical methods and applications
Lietuvos Matematikos Rinkinys, 2023 This article presents an overview of the results of solving the minimal surface equation by numerical methods. Another research task is the application of minimal surfaces in science, technology, especially architecture.
Mifodijus Sapagovas
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A Hölder estimate for entire solutions to the two-valued minimal surface equation [PDF]
, 2015 Leobardo Rosales
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Form-finding software and minimal surface equation: A comparative approach
, 2015 Jana Lipkovski, Aleksandar Lipkovski
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Entire solutions of the minimal surface equation
Journal of Differential Geometry, 1989 L. Simon
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Computing the area-minimizing surface by the Allen-Cahn equation with the fixed boundary
AIMS Mathematics, 2023 The Allen-Cahn equation is a famous nonlinear reaction-diffusion equation used to study geometric motion and minimal hypersurfaces. This link has been scrutinized to construct minimal surfaces for many years.
Dongsun Lee
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A Computational Model for q-Bernstein Quasi-Minimal Bézier Surface
Journal of Mathematics, 2022 A computational model is presented to find the q-Bernstein quasi-minimal Bézier surfaces as the extremal of Dirichlet functional, and the Bézier surfaces are used quite frequently in the literature of computer science for computer graphics and the ...
Daud Ahmad +5 more
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On the question of the smallest rolling resistance coefficient value of elastic wheel on a rigid horizontal surface [PDF]
E3S Web of Conferences, 2023 As is known, rolling resistance of an elastic wheel on a rigid support surface is determined by internal friction losses (hysteresis) in the wheel material and friction losses in the contact of wheel with support surface (friction losses in the hub ...
Mamaev Alexey +2 more
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An Application of Variational Minimization: Quasi-Harmonic Coons Patches
Journal of Function Spaces, 2022 For a minimal surface, the mean curvature of the surface vanishes for all possible parameterizations which results in a second-order nonlinear partial differential equation (pde), whose solution in general is the desired surface as the unknown function ...
Daud Ahmad +3 more
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A Level Set-Based Model for Image Segmentation under Geometric Constraints and Data Approximation
Journal of Imaging, 2023 In this paper, we propose a new model for image segmentation under geometric constraints. We define the geometric constraints and we give a minimization problem leading to a variational equation.
Guzel Khayretdinova +2 more
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