We find an equivalent condition for a real function f : [a, b] → R to be Lebesgue equivalent to an n-times differentiable function (n ≥ 2); a simple solution in the case n = 2 appeared in an earlier paper. For that purpose, we introduce the notions of CBV G1/n and SBV G1/n functions, which play analogous rôles for the n-th order differentiability as the classical notion of a V BG∗ function for ...

We prove a global fractional differentiability result via the Caccioppoli-type estimate for solutions to nonlinear elliptic problems with measure data. This work is inspired by recent paper [B. Avelin, T. Kuusi and G. Mingione, Arch. Ration

In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara different...

We consider a non-local Shrödinger problem driven by the fractional Orlicz g-Laplace operator as follows(P)(−△g)αu+g(u)=K(x)f(x,u),inRd, where d≥3,(−△g)α is operator, f:Rd×R→R measurable function and K positive continuous function. Employing Nehari manifold method without assuming well-known Ambrosetti-Rabinowitz differentiability conditions on non-linear term f, we prove that (P) has ground st...

For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous  differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.

We present a proof of strict g-convexity in 2D for solutions generated Jacobian equations with g-Monge–Ampère measure bounded away from 0. Subsequently this implies $$C^1$$ differentiability the case above. Our follows one given by Trudinger and Wang Monge–Ampère case. Thus, like theirs, our argument is local yields quantitative estimate on g-convexity. As result new even optimal transport case...

The modification of the Clarke generalized subdiNerentia1 due to Michel and Penot is a useful tool in determining differentiability properties for certain classes of real functions on a normed linear space. The Glteaux differentiability of any real function can be deduced from the GBteaux differentiability of the norm if the function has a directional derivative which attains a constant related...