The aim of this study is the approximation of a solution x* of a ganeralized equation 0 in f(x)+F(x) in Banach spaces, where f is a single-valued function whose second order Frechet derivative satisfies an Hölder condition and F stands for a set-valed map with closed graph. Using a fixed point theorem and the Aubin property of F, we show the existe...
We prove a new sharp Kolmogorov-type inequality that estimates the uniform norm of a mixed derivative of fractional order (in the sense of Marchaud) of a function of several variables via the uniform norm of the function and its norm on Hölder spaces.
Siberian Mathematical Journal
We construct Sobolev-Morrey type spaces with dominant mixed derivatives and, using the obtained integral representation, prove some embedding theorems in these spaces.
We consider a boundary value problem in the unit disk for an elliptic equation of order N with constant coefficients. We suppose, that the characteristic equation has exactly M pairs of complex conjugate roots (0 ≤ 2M ≤ N). The solution of this problem belongs to the class of N times continuously differentiable functions, which with up to the (N − ...
Annals of Global Analysis and Geometry
We show that every ‘conveniently Hölder’ homomorphism between Lie groups in the sense of convenient differential calculus is smooth (in the convenient sense). In particular, every ℓip0-homomorphism is smooth.