Die allgemeinen Sätze über den Zusammenhang der Functionen einer reellen Variabeln mit ihren Ableitungen
It is proved that real functions on which can be represented as the difference of two semiconvex functions with a general modulus (or of two lower -functions, or of two strongly paraconvex functions) coincide with semismooth functions on (i.e. those locally Lipschitz functions on for which and for each ). Further, for each modulus , we characterize the class of functions on which can be written as , where and are semiconvex with modulus (for some ) using a new notion of...
In the geometries of stratified groups, we provide differentiability theorems for both functions of bounded variation and Sobolev functions. Proofs are based on a systematic application of the Sobolev-Poincaré inequality and the so-called representation formula.