Zobrazeno 1 - 10
of 85
pro vyhledávání: '"Skrypnik, Igor i."'
In this work we prove that the non-negative functions $u \in L^s_{loc}(\Omega)$, for some $s>0$, belonging to the De Giorgi classes \begin{equation}\label{eq0.1} \fint\limits_{B_{r(1-\sigma)}(x_{0})} \big|\nabla \big(u-k\big)_{-}\big|^{p}\, dx \leqsl
Externí odkaz:
http://arxiv.org/abs/2403.13539
We prove the weak Harnack inequality for the functions $u$ which belong to the corresponding De Giorgi classes $DG^{-}(\Omega)$ under the additional assumption that $u\in L^{s}_{loc}(\Omega)$ with some $s> 0$. In particular, our result covers new cas
Externí odkaz:
http://arxiv.org/abs/2304.04499
We study the qualitative properties of functions belonging to the corresponding De Giorgi classes \begin{equation*} \int\limits_{B_{r(1-\sigma)}(x_{0})}\,\varPhi(x, |\nabla(u-k)_{\pm}|)\,dx \leqslant \gamma\,\int\limits_{B_{r}(x_{0})}\,\varPhi\bigg(x
Externí odkaz:
http://arxiv.org/abs/2210.02178
In this brief note we discuss local H\"older 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_i(x,u,\nabla u) \bigg) =0,$ for $x \in \Omega \subset \subset \mathb
Externí odkaz:
http://arxiv.org/abs/2206.06799
Publikováno v:
Advances in Nonlinear Analysis, vol. 12, no. 1, 2023, pp. 237-265
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 parabolic approach to expansion of positivity we obtain the interior H\"ol
Externí odkaz:
http://arxiv.org/abs/2109.07996
We prove the continuity of bounded solutions for a wide class of parabolic equations with $(p,q)$-growth $$ u_{t}-{\rm div}\left(g(x,t,|\nabla u|)\,\frac{\nabla u}{|\nabla u|}\right)=0, $$ under the generalized non-logarithmic Zhikov's condition $$ g
Externí odkaz:
http://arxiv.org/abs/2102.01550
We prove continuity and Harnack's inequality for bounded solutions to elliptic equations of the type $$ \begin{aligned} {\rm div}\big(|\nabla u|^{p-2}\,\nabla u+a(x)|\nabla u|^{q-2}\,\nabla u\big)=0,& \quad a(x)\geqslant0, \\ |a(x)-a(y)|\leqslant A|x
Externí odkaz:
http://arxiv.org/abs/2012.10960
We introduce elliptic and parabolic $\mathcal{B}_{1}$ classes that generalize the well-known $\mathfrak{B}_{p}$ classes of DeGiorgi, Ladyzhenskaya and Ural'tseva with $p>1$. New classes are applied to prove pointwise continuity of solutions of ellipt
Externí odkaz:
http://arxiv.org/abs/2006.05764
Publikováno v:
Advances in Nonlinear Analysis, Vol 12, Iss 1, Pp 237-265 (2022)
We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kind ∑i=1s∂iiu+∑i=s+1N∂i(Ai(x,u,∇u))=0,x∈Ω⊂⊂RNfor1≤s≤(N−1),\mathop{\sum }\limits_{i=1}^{s}{\partial }_{ii}u+\mathop
Externí odkaz:
https://doaj.org/article/0300f9efc3004defa669c72ad0e55a5b
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