23 citations · 37 across the 17 of their papers we have counts for
17 papers
On the weak Harnack inequality for unbounded non-negative super-solutions of degenerate double-phase parabolic equations
Mariia Savchenko, Igor Skrypnik, Yevgeniia Yevgenieva
In the case , we give a proof of the weak Harnack inequality for non-negative super-solutions of degenerate double-phase parabolic equations under the additiona…
A note on the weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth
Mariia O. Savchenko, Igor I. Skrypnik, Yevgeniia A. Yevgenieva
We prove the weak Harnack inequality for the functions which belong to the corresponding De Giorgi classes under the additional assumption that $u\in L^{s}_{loc}(Ω)…
Harnack's inequality for degenerate double phase parabolic equations under the non-logarithmic Zhikov's condition
Mariia Savchenko, Igor Skrypnik, Yevgeniia Yevgenieva
We prove Harnack's type inequalities for bounded non-negative solutions of degenerate parabolic equations with growth $$ u_{t}-{\rm div}\left(\mid \nabla u \mid^{p-2}\nabla…
Continuity and Harnack inequalities for local minimizers of non uniformly elliptic functionals with generalized Orlicz growth under the non-logarithmic conditions
Maria O. Savchenko, Igor I. Skrypnik, Yevgeniia A. Yevgenieva
We study the qualitative properties of functions belonging to the corresponding De Giorgi classes \begin{equation*} \int\limits_{B_{r(1-σ)}(x_{0})}\,\varPhi(x, |\nabla(u-k)_{\pm}|)…
On asymptotic behavior of solutions to non-uniformly elliptic equations with generalized Orlicz growth
O. V. Hadzhy, M. O. Savchenko, I. I. Skrypnik +1
We study asymptotic behavior of sub-solutions to non-uniformly elliptic equations with nonstandard growth. In particular, Harnack type inequalities are proved. Our approach gives n…
Harnack inequality for solutions of the -Laplace equation under the precise non-logarithmic Zhikov's conditions
Igor Skrypnik, Yevgeniia Yevgenieva
We prove continuity and Harnack's inequality for bounded solutions to the equation $$ {\rm div}\big(|\nabla u|^{p(x)-2}\,\nabla u \big)=0, \quad p(x)= p + L\frac{\log\log\frac{1}{|…
A note on the point-wise behaviour of bounded solutions for a non-standard elliptic operator
Laura Baldelli, Simone Ciani, Igor I. Skrypnik +1
In this brief note we discuss local Hölder continuity for solutions to anisotropic elliptic equations of the type $ \sum_{i=1}^s \partial_{ii} u+ \sum_{i=s+1}^N \partial_i \bigg(A_…
On the Local Behavior of Local Weak Solutions to some Singular Anisotropic Elliptic Equations
Simone Ciani, Igor I. Skrypnik, Vincenzo Vespri
We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations that involves both non-degenerate and singular operators. Throughout a para…
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…
Estimates of solutions for the parabolic -Laplacian equation with measure via parabolic nonlinear potentials
Vitali Liskevich, Igor I. Skrypnik, Zeev Sobol
For weak solutions to the evolutional -Laplace equation with a time-dependent Radon measure on the right hand side we obtain pointwise estimates via a nonlinear parabolic potent…
Pointwise estimates for solutions of singular quasi-linear parabolic equations
Vitali Liskevich, Igor I. Skrypnik
For a class of singular divergence type quasi-linear parabolic equations with a Radon measure on the right hand side we derive pointwise estimates for solutions via the nonlinear W…
Potential estimates for quasi-linear parabolic equations
Vitali Liskevich, Igor I. Skrypnik, Zeev Sobol
For a class of divergence type quasi-linear degenerate parabolic equations with a Radon measure on the right hand side we derive pointwise estimates for solutions via nonlinear Wol…
Gradient estimates for degenerate quasi-linear parabolic equations
Vitali Liskevich, Igor I. Skrypnik, Zeev Sobol
For a general class of divergence type quasi-linear degenerate parabolic equations with differentiable structure and lower order coefficients form bounded with respect to the Lapla…
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…