Eventual regularity for the parabolic minimal surface equation [PDF]
, 2015 We show that the parabolic minimal surface equation has an eventual regularization effect, that is, the solution becomes smooth after a (strictly positive) finite time.
Giovanni Bellettini +2 more
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Symmetric solutions of the singular minimal surface equation [PDF]
Annals of Global Analysis and Geometry, 2021 We classify all rotational symmetric solutions of the singular minimal surface equation in both cases α0$$\end{document}. In addition, we discuss further geometric and analytic properties of the solutions, in particular stability, minimizing properties ...
Ulrich Dierkes, Nico Groh
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Survey on the Asymptotic Dirichlet Problem for the Minimal Surface Equation [PDF]
Minimal Surfaces: Integrable Systems and Visualisation, 2021 We give a survey on the development of the study of the asymptotic Dirichlet problem for the minimal surface equation on Cartan-Hadamard manifolds. Part of this survey is based on the introductory part of the doctoral dissertation of the author.
Esko Heinonen
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On the growth of solutions to the minimal surface equation over domains containing a halfplane [PDF]
, 2013 We consider minimal graphs $$u = u(x,y) > 0$$u=u(x,y)>0 over unbounded domains D with $$u = 0$$u=0 on $$\partial D$$∂D. Assuming D contains a sector properly containing a halfplane, we show that u grows at most linearly.
Erik Lundberg, Allen Weitsman
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The Dirichlet problem for the minimal surface equation, with infinite data [PDF]
, 1966 takes the boundary values plus infinity on the vertical sides of the square \x\ then the arc must necessarily be straight. This being the case, the most general boundary value problem with infinite data takes the following form. Let D be a bounded convex
Howard Jenkins, James Serrin
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On solutions of the singular minimal surface equation [PDF]
Annali di Matematica Pura ed Applicata, 2018 Ulrich Dierkes
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A remark on global existence for small initial data of the minimal surface equation in Minkowskian space time [PDF]
, 2003 We show that the nonlinear wave equation corresponding to the minimal surface equation in Minkowski space time has a global solution for sufficiently small initial data.
Hans Lindblad
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An inverse problem for the Riemannian minimal surface equation
Journal of Differential Equations, 2023 Cătălin I. Cârstea +3 more
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A Free Boundary Problem for Minimal Surface Equation [PDF]
, 1991 In this note we introduced a free boundary problem for minimal surface equation. The following variational problem had been treated by H.W.Alt, L.A.Caffarelli and A.Freedman $[1],[2] $: $\{\begin{array}{l}\int_{\Omega}(F(|\nabla u|^{2})+Q^{2}\chi_{u>0}
Yoshihiko Yamaura
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On uniform convergence of piecewise-linear solutions to minimal surface equation [PDF]
, 2014 Mikhail Andreevich Gatsunaev +1 more
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