23 citations · 37 across the 17 of their papers we have counts for
4 papers · 1 filter
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_…