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The Dirichlet problem for the $$\alpha $$α-singular minimal surface equation [PDF]
Archiv der Mathematik, 2018 Let $$\Omega \subset \mathbb {R}^n$$Ω⊂Rn be a bounded mean convex domain. If $$\alpha
R. López
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On solutions of the singular minimal surface equation [PDF]
Annali di Matematica Pura ed Applicata (1923 -), 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
U. Dierkes
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Global existence for the minimal surface equation on ℝ^{1,1} [PDF]
, 2017 In a 2004 paper, Lindblad demonstrated that the minimal surface equation on $\mathbb{R}l^{1,1}$ describing graphical time-like minimal surfaces embedded in $\mathbb{R}^{1,2}$ enjoy small data global existence for compactly supported initial data, using ...
Willie Wong
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Phragmén-Lindelöf theorem for the minimal surface equation [PDF]
Proceedings of the American Mathematical Society, 1988 It is proved that if u u satisfies the minimal surface equation in an unbounded domain Ω \Omega which is properly contained in a half plane, then the growth property of u u depends on Ω \Omega and the boundary value of u u only.
Jenn-Fang Hwang
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Eventual regularity for the parabolic minimal surface equation [PDF]
Discrete and Continuous Dynamical Systems, 2014 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.
G. Bellettini, M. Novaga, G. Orlandi
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Growth Property for the Minimal Surface Equation in Unbounded Domains [PDF]
Proceedings of the American Mathematical Society, 1994 Here we prove that if u satisfies the minimal surface equation in an unbounded domain Ω \Omega which is properly contained in a half plane, then the growth rate of u is of the same order as the shape of Ω \Omega and u | ∂
Jenn-Fang Hwang
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The nonhomogeneous minimal surface equation involving a measure [PDF]
Pacific Journal of Mathematics, 1995 We find existence of a minimum in BV for the variational problem associated with \(\text{div } A(Du)+ \mu= 0\), where \(A\) is a mean curvature type operator and \(\mu\) a nonnegative measure satisfying a suitable growth condition. We then show a local \(L^ \infty\) estimate for the minimum.
William P. Ziemer
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The Dirichlet problem for the minimal surface equation, with possible infinite boundary data, over domains in a Riemannian surface [PDF]
, 2010 In this paper, we study the existence and uniqueness of solutions to Jenkins–Serrin type problems on domains in a Riemannian surface: infinite boundary data are allowed. In the case of unbounded domains, the study is focused on the hyperbolic plane.
L. Mazet, M. M. Rodríguez, H. Rosenberg
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, 1997 The minimal surface equation (MSE) for functions u: Ω → ℝ, Ω a domain of ℝ2, can be written $$\left( {1 + u_{}^2} \right){u_{xx}} - 2{u_x}{u_y}{u_{xy}} + \left( {1 + u_x^2} \right){u_{yy}} = 0$$ or equivalently \( {u_{xx}} + {u_{yy}} - {\left( {1 + |Du{|^2}} \right)^{ - 1}}\left( {u_x^2{u_{xx}} + 2{u_x}{u_y}{u_{xy}} + u_y^2{u_{yy}}} \right) = 0\)
L. Simon
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Phragmèn–Lindelöf theorem for minimal surface equations in higher dimensions [PDF]
Pacific Journal of Mathematics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chun-Chung Hsieh +2 more
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