The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Ulrich Dierkes - One of the best experts on this subject based on the ideXlab platform.
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Removable Singularities of Solutions of the Symmetric Minimal Surface Equation
Vietnam Journal of Mathematics, 2020Co-Authors: Ulrich DierkesAbstract:We show that compact sets of ( n − 1)-dimensional Hausdorff measure zero constitute removable singularities for weak solutions of the singular and symmetric Minimal Surface Equation. These results comprise Minimal Surfaces in hyperbolic space and “heavy” Minimal Surfaces in gravitational fields.
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on solutions of the singular Minimal Surface Equation
Annali di Matematica Pura ed Applicata, 2019Co-Authors: Ulrich DierkesAbstract:Results of Bernstein type are proven for supersolutions of the singular Minimal Surface Equation when $$\alpha <0$$ . In particular the non-existence of “entire” Minimal graphs in hyperbolic space is shown. In addition we construct a foliation of $$\mathbb {R}^n\times \mathbb {R}^+$$ consisting of minimizing Surfaces, and solve a Dirichlet problem for the singular Minimal Surface Equation.
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On solutions of the singular Minimal Surface Equation
Annali di Matematica Pura ed Applicata (1923 -), 2018Co-Authors: Ulrich DierkesAbstract:Results of Bernstein type are proven for supersolutions of the singular Minimal Surface Equation when $$\alpha
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Bernstein results for symmetric Minimal Surfaces of controlled growth
Annali Della Scuola Normale Superiore Di Pisa-classe Di Scienze, 2018Co-Authors: Ulrich Dierkes, Tobias TennstädtAbstract:We prove that there is no entire solution of the symmetric Minimal Surface Equation which is of sublinear growth. This result is extended to parametric and non-parametric minimizers of the corresponding variational integral
Hans Lindblad - One of the best experts on this subject based on the ideXlab platform.
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a remark on global existence for small initial data of the Minimal Surface Equation in minkowskian space time
Proceedings of the American Mathematical Society, 2003Co-Authors: Hans LindbladAbstract: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.
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a remark on global existence for small initial data of the Minimal Surface Equation in minkowskian space time
arXiv: Analysis of PDEs, 2002Co-Authors: Hans LindbladAbstract:We show that the nonlinear wave Equation corresponding to the Minimal Surface Equation in Minkowski space time has global solutions for sufficiently small initial data. This is an interesting model in Lorentziann and is also the Equation for a membrane in field theory.
Jenn-fang Hwang - One of the best experts on this subject based on the ideXlab platform.
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how many theorems can be derived from a vector function on uniqueness theorems for the Minimal Surface Equation
Taiwanese Journal of Mathematics, 2003Co-Authors: Jenn-fang HwangAbstract:In this survey article we consider Equations related to the Minimal Surface Equation div Tu = 0, where Tu = ∇u √1+|∇u|2 , ∇u is the gradient of u, and derive some structural inequalities related to the vector function Tu. These structural inequalities give rise to striking uniqueness properties of the solutions.
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Phragmèn–Lindelöf theorem for Minimal Surface Equations in higher dimensions
Pacific Journal of Mathematics, 2002Co-Authors: Chun-chung Hsieh, Jenn-fang Hwang, Fei-tsen LiangAbstract:Here we prove that if u satisfies the Minimal Surface Equation in an unbounded domain which is properly contained in a half space of R n , with n > 2, then the growth rate of u is of the same order as that of the shape of fl and the boundary value of u.
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CATENOID-LIKE SOLUTIONS FOR THE Minimal Surface Equation
Pacific Journal of Mathematics, 1998Co-Authors: Jenn-fang HwangAbstract:where Tu = Du √ 1 + |Du|2 and Du = (ux, uy). In 1965, Nitsche [5] announced the following result: “Let Ωα ⊂ R be a sector with angle 0 < α < π. If u satisfies the Minimal Surface Equation with vanishing boundary value in Ωα, then u ≡ 0”. Hwang extends this result in [3], [4] and proves that, in an unbounded domain Ω properly contained in the half plane in R, if u satisfies the Minimal Surface Equation, then, the growth property of u is determined completely by the shape of Ω and the boundary value of u. In this respect, the Phragmen-Lindelof theorem for the Minimal Surface Equation is better than that for the Laplace Equation; (indeed, if u satisfies the Laplace Equation in an unbounded domain Ω, the growth property of u cannot be determined completely by the shape of Ω and the boundary data of u alone [8]). One of the results in [4] is the following:
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Growth property for the Minimal Surface Equation in unbounded domains
Proceedings of the American Mathematical Society, 1994Co-Authors: Jenn-fang HwangAbstract:Here we prove that if u satisfies the Minimal Surface Equation in an unbounded domain Q which is properly contained in a half plane, then the growth rate of u is of the same order as the shape of Q and ulan .
Yuzhu Wang - One of the best experts on this subject based on the ideXlab platform.
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global existence of classical solutions to the Minimal Surface Equation with slow decay initial value
Applied Mathematics and Computation, 2010Co-Authors: Yuzhu Wang, Yinxia WangAbstract:In this paper, we prove that the global existence of classical solutions to the Cauchy problem for the Minimal Surface Equation with slow decay initial value in Minkowskian space time.
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Global existence of classical solutions to the Minimal Surface Equation in two space dimensions with slow decay initial value
Journal of Mathematical Physics, 2009Co-Authors: Yuzhu WangAbstract:In this paper, we prove the global existence of classical solutions to the Cauchy problem for the Minimal Surface Equation in the Minkowski space R1+2 with slow decay initial value.
A. V. Pokrovskii - One of the best experts on this subject based on the ideXlab platform.
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On Singular Points of Solutions of the Minimal Surface Equation on Sets of Positive Measure
Functional Analysis and Its Applications, 2018Co-Authors: A. V. PokrovskiiAbstract:It is shown that, for any compact set K ⊂ ℝ n (n ⩾ 2) of positive Lebesgue measure and any bounded domain G ⊃ K, there exists a function in the Holder class C1,1(G) that is a solution of the Minimal Surface Equation in G \ K and cannot be extended from G \ K to G as a solution of this Equation.
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Removable singularities of solutions of elliptic Equations
Journal of Mathematical Sciences, 2009Co-Authors: A. V. PokrovskiiAbstract:This paper is an overview of results devoted to metric conditions for removability of closed sets for solutions of homogeneous partial differential Equations in various function classes. The author considers Equations with a quasi-homogeneous semi-elliptic operator and with constant coefficients, linear second-order uniformly elliptic Equations in the divergent form with real bounded measurable coefficients, quasilinear Equations with the p-Laplacian, and the Minimal Surface Equation. A number of results is published for the first time.
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Removable Singularities of Solutions of the Minimal Surface Equation
Functional Analysis and Its Applications, 2005Co-Authors: A. V. PokrovskiiAbstract:Suppose that G is a bounded domain in ℝ^ n ( n ⩾ 2), E ≠ G is a relatively closed set in G , and 0 < α < 1. We prove that E is removable for solutions of the Minimal Surface Equation in the class C ^1,α( G )_loc if and only if the ( n − 1 + α)-dimensional Hausdorff measure of E is zero.