Approximate continuity and differentiability with respect to density degree, an application to BV and Sobolev functions

DOI10.1007/s10476-022-0178-yOpenAlexW4310207256MaRDI QIDQ2678405

Silvano Delladio

Publication date: 23 January 2023

Published in: Analysis Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10476-022-0178-y

zbMATH Keywords

function of bounded variationSobolev functionapproximately continuous functionapproximately differentiable functionpoints of Lebesgue density\(m\)-approximately continuous function\(m\)-approximately differentiable functionpoints of Lebesgue m-densityw

Mathematics Subject Classification ID

Weak and generalized continuity (54C08) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuity and differentiation questions (26B05) Functions of bounded variation, generalizations (26A45) Classical measure theory (28Axx)

Related Items (4)

A closure result for differential forms in the context of superdensity, approximation of measurable functions by density-degree functions ⋮ \(m\)-approximate Taylor polynomial ⋮ Generalized densities on \(\mathbb{R}^n\) and their applications ⋮ A fine property of sets at points of Lebesgue density

Cites Work

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• Functions of class \(C^1\) subject to a Legendre condition in an enhanced density set
• Fine topology methods in real analysis and potential theory
• Structure of tangencies to distributions via the implicit function theorem
• Structure of prescribed gradient domains for non-integrable vector fields
• Some new results about the geometry of sets of finite perimeter
• A NOTE ON SOME TOPOLOGICAL PROPERTIES OF SETS WITH FINITE PERIMETER
• A SHORT NOTE ON ENHANCED DENSITY SETS
• Weakly Differentiable Functions
• Size of tangencies to non-involutve distributions
• The tangency of a C^1 smooth submanifold with respect to a non-involutive C^1 distribution has no superdensity points
• A note on a generalization of the Schwarz theorem about the equality of mixed partial derivatives

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