Displaying similar documents to “Barriers for a class of geometric evolution problems”

Uniqueness of minimal projections onto two-dimensional subspaces

Boris Shekhtman, Lesław Skrzypek (2005)

Studia Mathematica

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We prove that minimal projections from L p (1 < p < ∞) onto any two-dimensional subspace are unique. This result complements the theorems of W. Odyniec ([OL, Theorem I.1.3], [O3]). We also investigate the minimal number of norming points for such projections.

Constants of strong uniqueness of minimal norm-one projections

A. Micek (2011)

Banach Center Publications

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In this paper we calculate the constants of strong uniqueness of minimal norm-one projections on subspaces of codimension k in the space l ( n ) . This generalizes a main result of W. Odyniec and M. P. Prophet [J. Approx. Theory 145 (2007), 111-121]. We applied in our proof Kolmogorov’s type theorem (see A. Wójcik [Approximation and Function Spaces (Gdańsk, 1979), PWN, Warszawa / North-Holland, Amsterdam, 1981, 854-866]) for strongly unique best approximation.

Noninvertible minimal maps

Sergiĭ Kolyada, L&amp;#039;ubomír Snoha, Sergeĭ Trofimchuk (2001)

Fundamenta Mathematicae

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For a discrete dynamical system given by a compact Hausdorff space X and a continuous selfmap f of X the connection between minimality, invertibility and openness of f is investigated. It is shown that any minimal map is feebly open, i.e., sends open sets to sets with nonempty interiors (and if it is open then it is a homeomorphism). Further, it is shown that if f is minimal and A ⊆ X then both f(A) and f - 1 ( A ) share with A those topological properties which describe how large a set is. Using...

Uniqueness for unbounded solutions to stationary viscous Hamilton-Jacobi equations

Guy Barles, Alessio Porretta (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider a class of stationary viscous Hamilton-Jacobi equations aswhere λ 0 , A ( x ) is a bounded and uniformly elliptic matrix and H ( x , ξ ) is convex in ξ and grows at most like | ξ | q + f ( x ) , with 1 &lt; q &lt; 2 and f L N / q ' ( Ω ) . Under such growth conditions solutions are in general unbounded, and there is not uniqueness of usual weak solutions. We prove that uniqueness holds in the restricted class of solutions satisfying a suitable energy-type estimate, ( 1 + | u | ) q ¯ - 1 u H 0 1 ( Ω ) , for a certain (optimal) exponent q ¯ . This completes the...

Induced subsystems associated to a Cantor minimal system

Heidi Dahl, Mats Molberg (2009)

Colloquium Mathematicae

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Let (X,T) be a Cantor minimal system and let (R,) be the associated étale equivalence relation (the orbit equivalence relation). We show that for an arbitrary Cantor minimal system (Y,S) there exists a closed subset Z of X such that (Y,S) is conjugate to the subsystem (Z,T̃), where T̃ is the induced map on Z from T. We explore when we may choose Z to be a T-regular and/or a T-thin set, and we relate T-regularity of a set to R-étaleness. The latter concept plays an important role in the...

Hölder regularity of two-dimensional almost-minimal sets in n

Guy David (2009)

Annales de la faculté des sciences de Toulouse Mathématiques

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We give a different and probably more elementary proof of a good part of Jean Taylor’s regularity theorem for Almgren almost-minimal sets of dimension 2 in 3 . We use this opportunity to settle some details about almost-minimal sets, extend a part of Taylor’s result to almost-minimal sets of dimension 2 in n , and give the expected characterization of the closed sets E of dimension 2 in 3 that are minimal, in the sense that H 2 ( E F ) H 2 ( F E ) for every closed set F such that there is a bounded set B so...

Cylinder cocycle extensions of minimal rotations on monothetic groups

Mieczysław K. Mentzen, Artur Siemaszko (2004)

Colloquium Mathematicae

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The main results of this paper are: 1. No topologically transitive cocycle m -extension of minimal rotation on the unit circle by a continuous real-valued bounded variation ℤ-cocycle admits minimal subsets. 2. A minimal rotation on a compact metric monothetic group does not admit a topologically transitive real-valued cocycle if and only if the group is finite.