1 citations · 2 across the 6 of their papers we have counts for
6 papers
Continuity and Harnack inequalities for local minimizers of non uniformly elliptic functionals with generalized Orlicz growth under the non-logarithmic conditions
Maria O. Savchenko, Igor I. Skrypnik, Yevgeniia A. Yevgenieva
We study the qualitative properties of functions belonging to the corresponding De Giorgi classes \begin{equation*} \int\limits_{B_{r(1-σ)}(x_{0})}\,\varPhi(x, |\nabla(u-k)_{\pm}|)…
On the continuity of solutions of quasilinear parabolic equations with generalized Orlicz growth under non-logarithmic conditions
Igor I. Skrypnik, Mykhailo V. Voitovych
We prove the continuity of bounded solutions for a wide class of parabolic equations with -growth $$ u_{t}-{\rm div}\left(g(x,t,|\nabla u|)\,\frac{\nabla u}{|\nabla u|}\righ…
Interior continuity, continuity up to the boundary and Harnack's inequality for double-phase elliptic equations with non-logarithmic conditions
Oleksandr V. Hadzhy, Igor I. Skrypnik, Mykhailo V. Voitovych
We prove continuity and Harnack's inequality for bounded solutions to elliptic equations of the type $$ \begin{aligned} {\rm div}\big(|\nabla u|^{p-2}\,\nabla u+a(x)|\nabla u|^{q-2…
Harnack's inequality for quasilinear elliptic equations with generalized Orlicz growth
M. A. Shan, I. I. Skrypnik, M. V. Voitovych
We prove Harnack's inequality for bounded weak solutions to quasilinear second order elliptic equations with generalized Orlicz growth conditions. Our approach covers new cases of…
classes of DeGiorgi-Ladyzhenskaya-Ural'tseva and their applications to elliptic and parabolic equations with generalized Orlicz growth conditions
Igor I. Skrypnik, Mykhailo V. Voitovych
We introduce elliptic and parabolic classes that generalize the well-known classes of DeGiorgi, Ladyzhenskaya and Ural'tseva with . New cl…
Harnack inequality and continuity of solutions to quasi-linear degenerate parabolic equations with coeffcients from Kato-type classes
Vitali Liskevich, Igor I. Skrypnik
For a general class of divergence type quasi-linear degenerate parabolic equations with measurable coeffcients and lower order terms from non-linear Kato-type classes, we prove loc…