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Proceedings of the Royal Society of Edinburgh Section A: Mathematics, ISSN 0308-2105, 02/2018, Volume 148, Issue 1, pp. 33 - 50
Functions of bounded deformation (BD) arise naturally in the study of fracture and damage in a geometrically linear context. They are related to functions of... 
bounded deformation | bounded variation | Caccioppoli partition | approximate continuity | MATHEMATICS, APPLIED | DENSITY RESULT | APPROXIMATION | INEQUALITY | RELAXATION | LINEARIZED ELASTICITY | BRITTLE-FRACTURE | CONVEX-FUNCTIONS | MATHEMATICS | GLOBAL METHOD | ENERGIES | PLASTICITY | Continuity (mathematics) | Deformation | Analysis of PDEs | Mathematics
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 12/2018, Volume 468, Issue 2, pp. 1131 - 1143
In this paper, we provide upper and lower estimates for the minimal number of functions needed to represent a bounded variation function with an accuracy of... 
Bounded variation functions | The epsilon-entropy | MATHEMATICS | RATES | MATHEMATICS, APPLIED | COMPACTNESS | ENTROPY
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2019, Volume 479, Issue 1, pp. 482 - 530
We study properties of functions with bounded variation in Carnot-Carathéodory spaces. We prove their almost everywhere approximate differentiability and we... 
Functions with bounded variation | Carnot-Carathéodory spaces | MATHEMATICS, APPLIED | INEQUALITIES | Carnot-Caratheodory spaces | BV FUNCTIONS | VECTOR-FIELDS | SOBOLEV | MATHEMATICS | SUBMANIFOLDS | REGULARITY | THEOREMS | SETS | RECTIFIABILITY | PERIMETER
Journal Article
Miskolc Mathematical Notes, ISSN 1787-2405, 2018, Volume 19, Issue 1, pp. 157 - 170
In this paper we introduce a function space with some generalization of bounded variation and study some of its properties, like embeddings, decompositions and... 
Riesz p-variation | Bounded variation spaces | MATHEMATICS | bounded variation spaces
Journal Article
Geometric and Functional Analysis, ISSN 1016-443X, 8/2019, Volume 29, Issue 4, pp. 1235 - 1294
Extending the notion of bounded variation, a function $$u \in L_c^1(\mathbb {R}^n)$$ u ∈ L c 1 ( R n ) is of bounded fractional variation with respect to some... 
Flat chains | 28A75 | Bounded variation | Analysis | Change of variables | 49Q15 | 26A16 | Mathematics | Fractals | Currents | MATHEMATICS | G CHAINS
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 08/2017, Volume 290, Issue 11-12, pp. 1830 - 1839
The aim of this short note is to give an alternative proof, which applies to functions of bounded variation in arbitrary domains, of an inequality by Maz'ya... 
Friedrichs inequality | Primary: 46E35; Secondary: 49Q15 | extension | trace | Functions of bounded variation | MATHEMATICS | Equality | Mathematics - Analysis of PDEs
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2018, Volume 459, Issue 2, pp. 861 - 878
In this work it is studied a quasilinear elliptic problem in the whole space RN involving the 1-Laplacian operator, with potentials which can vanish at... 
Mountain pass theorem | Bounded variation functions | 1-Laplacian | MATHEMATICS | MATHEMATICS, APPLIED | LINEAR GROWTH | NONLINEAR SCHRODINGER-EQUATIONS | OPERATOR | FUNCTIONALS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2020, Volume 484, Issue 2, p. 123752
The main goal of this paper is to prove a compactness criterion for subsets of the Banach space of functions of bounded variation in the sense of Jordan. In... 
Quasimeasure of noncompactness | Functions of bounded variation | Variation in the sense of Jordan | Compact set | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 07/2016, Volume 271, Issue 1, pp. 37 - 48
Defect of compactness for non-compact imbeddings of Banach spaces can be expressed in the form of a profile decomposition. Let X be a Banach space continuously... 
1-Laplacian | Functions of bounded variation | Subelliptic Sobolev spaces | Concentration compactness | MATHEMATICS | Naturvetenskap | Mathematics | Natural Sciences | Matematik
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 08/2019, Volume 69, Issue 4, pp. 833 - 842
The aim of this paper is to bring together two areas of studies in the theory of analytic functions: functions of bounded variation and functions related to... 
analytic functions | univalent functions | conic domain | Primary 30C45 | MATHEMATICS | CONVEX | Domains | Analytic functions | Mathematical analysis
Journal Article
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, ISSN 1435-9855, 2018, Volume 20, Issue 8, pp. 1819 - 1850
We prove continuity and surjectivity of the trace map onto L-p(R-n), from a space of functions of locally bounded variation, defined by the Carleson... 
bounded variation | MATHEMATICS | Corona Theorem | MATHEMATICS, APPLIED | Carleson functional | SPACES | MAXIMAL-FUNCTION | stopping time argument | Extension map | OPERATORS | approximability | elliptic equation
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1, pp. 1 - 16
In this paper we obtain sharp Ostrowski type inequalities for multidimensional sets of bounded variation and multivariate functions of bounded variation. 
sets of bounded variation | multivariate functions of bounded variation | Ostrowski type inequalities | MATHEMATICS | MATHEMATICS, APPLIED | Functions (mathematics) | Inequalities | 41A44 | 41A63 | Research | 26D15 | 41A17
Journal Article
Advances in Applied Probability, ISSN 0001-8678, 12/2016, Volume 48, Issue 4, pp. 947 - 971
Journal Article
Georgian Mathematical Journal, ISSN 1072-947X, 09/2016, Volume 23, Issue 3, pp. 417 - 427
The idea of functions of bounded differential variation was introduced by Bhatt, Dabhi and Kachhia in [ ]. In the present paper, we introduce functions of... 
functions of bounded variation | 46J10 | 26A45 | 26A33 | functions of bounded differential variation | Caputo fractional derivative | Functions of bounded fractional differential variation | Functions of bounded differential variation | Functions of bounded variation
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2015, Volume 423, Issue 1, pp. 521 - 537
In the setting of a metric space equipped with a doubling measure and supporting a Poincaré inequality, and based on results by Björn and Shanmugalingam (2007)... 
Extension | Uniform domain | Jump set | Boundary trace | Bounded variation | Locality | MATHEMATICS | MATHEMATICS, APPLIED | BV FUNCTIONS | EXTENDABILITY | PERIMETER
Journal Article
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