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Subjects
26-XX Real functions
26Bxx Functions of several variables
26B05 Continuity and differentiation questions

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Displaying 1 – 9 of 9

$C^{1}$ extensions of functions and stabilization of Glaeser refinements.

B. Klartag, N. Zobin (2007)

Revista Matemática Iberoamericana

Complément de Schur et sous-différentiel du second ordre d'une fonction convexe.

Alberto Seeger (1991)

Aequationes mathematicae

Complements, approximations, smoothings and invariance properties.

Clarke, F.H., Ledyaev, Yu.S., Stern, R.J. (1997)

Journal of Convex Analysis

Complexity of the class of Peano functions

K. Omiljanowski, S. Solecki, J. Zielinski (2000)

Colloquium Mathematicae

We evaluate the descriptive set theoretic complexity of the space of continuous surjections from $ℝ^{m}$ to $ℝ^{n}$ .

Computation of Lojasiewicz Exponent of ...(x, y)

Tzee-Char Kuo (1974)

Commentarii mathematici Helvetici

Conception optimale ou identification de formes, calcul rapide de la dérivée directionnelle de la fonction coût

Jean Cea (1986)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Continuity of monotone functions

Boris Lavrič (1993)

Archivum Mathematicum

It is shown that a monotone function acting between euclidean spaces $R^{n}$ and $R^{m}$ is continuous almost everywhere with respect to the Lebesgue measure on $R^{n}$ .

Continuity of order-preserving functions

Boris Lavrič (1997)

Commentationes Mathematicae Universitatis Carolinae

Let the spaces $𝐑^{m}$ and $𝐑^{n}$ be ordered by cones $P$ and $Q$ respectively, let $A$ be a nonempty subset of $𝐑^{m}$ , and let $f : A ⟶ 𝐑^{n}$ be an order-preserving function. Suppose that $P$ is generating in $𝐑^{m}$ , and that $Q$ contains no affine line. Then $f$ is locally bounded on the interior of $A$ , and continuous almost everywhere with respect to the Lebesgue measure on $𝐑^{m}$ . If in addition $P$ is a closed halfspace and if $A$ is connected, then $f$ is continuous if and only if the range $f (A)$ is connected.

Convergence on almost every line for functions with gradient in $L^{p} (𝐑^{n})$

Charles Fefferman (1974)

Annales de l'institut Fourier

We prove that if $grad (f) \in L^{p} (R^{n})$ for certain values of $p$ , then $lim_{x_{1} \to \infty} f (x_{1}, x_{2}, ..., x_{n}) = const., a.e. in R^{n - 1} .$

Currently displaying 1 – 9 of 9

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