Comparison results between minimal barriers and viscosity solutions for geometric evolutions
Giovanni Bellettini, Matteo Novaga (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Giovanni Bellettini, Matteo Novaga (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Boris Shekhtman, Lesław Skrzypek (2005)
Studia Mathematica
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We prove that minimal projections from (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.
E. Barozzi, I. Tamanini (1985)
Rendiconti del Seminario Matematico della Università di Padova
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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 . 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.
Sergiĭ Kolyada, L&#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 share with A those topological properties which describe how large a set is. Using...
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 , is a bounded and uniformly elliptic matrix and is convex in and grows at most like , with and . 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, , for a certain (optimal) exponent . This completes the...
V. Caselles, M. Novaga, A. Chambolle (2010)
Rendiconti del Seminario Matematico della Università di Padova
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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...
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 in . 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 in , and give the expected characterization of the closed sets of dimension in that are minimal, in the sense that for every closed set such that there is a bounded set so...
Mieczysław K. Mentzen, Artur Siemaszko (2004)
Colloquium Mathematicae
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The main results of this paper are: 1. No topologically transitive cocycle -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.