About a man and lions
Absolutely continuous functions of several variables and diffeomorphisms
In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.
Absolutely continuous functions of two variables in the sense of Carathéodory.
Abstract superposition operators on mappings of bounded variation of two real variables. II.
Abstract superposition operators on mappings of bounded variation of two real variables. I.
Addendum to the paper "Generalizations to monotonicity for uniform convergence of double sine integrals over ℝ̅ ²₊" (Studia Math. 201 (2010), 287-304)
Affine and convex functions with respect to the logarithmic mean
The class of all functions f:(0,∞) → (0,∞) which are continuous at least at one point and affine with respect to the logarithmic mean is determined. Some related results concerning the functions convex with respect to the logarithmic mean are presented.
Algebraische Beschreibung der Ableitung bei -Mal Stetig-Differenzierbaren Funktionen
Almost classical solutions of Hamilton-Jacobi equations.
An analog of Sard's theorem for -smooth functions of two variables.
An approximation theorem for sequences of linear strains and its applications
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in by the sequence of linear strains of mapping bounded in Sobolev space . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.
An approximation theorem for sequences of linear strains and its applications
We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in L1 by the sequence of linear strains of mapping bounded in Sobolev space W1,p . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.
An axiomatic theory of non-absolutely convergent integrals in Rn
We introduce an axiomatic approach to the theory of non-absolutely convergent integrals. The definition of our ν-integral will be descriptive and depends mainly on characteristic null conditions. By specializing our concepts we will later obtain concrete theories of integration with natural properties and very general versions of the divergence theorem.
An Egoroff-type theorem for set-valued measurable functions.
An embedding theorem for Sobolev type functions with gradients in a Lorentz space
The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.
An example of a function, which is not a d.c. function
Let , . We construct a function which has Lipschitz Fréchet derivative on but is not a d.c. function.
An example of a -smooth function whose gradient range is an arc with no tangent at any point.
An implicit-function theorem for a class of monotone generalized equations
An incompatibility theorem
An integral defined by approximating partitions of unity