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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 study the boundary behavior of solutions to parabolic double-phase equations through the celebrated Wiener's sufficiency criterion. The analysis is conducted for cylindrical domains and the regularity up to the lateral boundary is shown in terms o
Externí odkaz:
http://arxiv.org/abs/2403.06550
We study the decay towards the extinction that pertains to local weak solutions to fully anisotropic equations whose prototype is \[ \partial_t u= \sum_{i=1}^N \partial_i (|\partial_i u|^{p_i-2} \partial_i u), \qquad 1
Externí odkaz:
http://arxiv.org/abs/2309.05022
In the case $q> p\dfrac{n+2}{n}$, we give a proof of the weak Harnack inequality for non-negative super-solutions of degenerate double-phase parabolic equations under the additional assumption that $u\in L^{s}_{loc}(\Omega_{T})$ with some $s >p\dfrac
Externí odkaz:
http://arxiv.org/abs/2305.13053
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 prove Harnack's type inequalities for bounded non-negative solutions of degenerate parabolic equations with $(p,q)$ growth $$ u_{t}-{\rm div}\left(\mid \nabla u \mid^{p-2}\nabla u + a(x,t) \mid \nabla u \mid^{q-2}\nabla u \right)=0,\quad a(x,t) \g
Externí odkaz:
http://arxiv.org/abs/2301.08501
We study the qualitative properties of functions belonging to the corresponding De Giorgi classes \begin{equation*} \int\limits_{B_{r(1-\sigma)}(x_{0})}\,\varPhi(x, |\nabla(u-k)_{\pm}|)\,dx \leqslant \gamma\,\int\limits_{B_{r}(x_{0})}\,\varPhi\bigg(x
Externí odkaz:
http://arxiv.org/abs/2210.02178
We study asymptotic behavior of sub-solutions to non-uniformly elliptic equations with nonstandard growth. In particular, Harnack type inequalities are proved. Our approach gives new results for the cases with (p,q) nonlinearity and generalized Orlic
Externí odkaz:
http://arxiv.org/abs/2208.05671
Autor:
Skrypnik, Igor, Yevgenieva, Yevgeniia
We prove continuity and Harnack's inequality for bounded solutions to the equation $$ {\rm div}\big(|\nabla u|^{p(x)-2}\,\nabla u \big)=0, \quad p(x)= p + L\frac{\log\log\frac{1}{|x-x_{0}|}}{\log\frac{1}{|x-x_{0}|}},\quad L > 0, $$ under the precise
Externí odkaz:
http://arxiv.org/abs/2208.01970
Autor:
Iskandar Azmy Harahap, Małgorzata Moszak, Magdalena Czlapka-Matyasik, Katarzyna Skrypnik, Paweł Bogdański, Joanna Suliburska
Publikováno v:
Frontiers in Nutrition, Vol 11 (2024)
BackgroundMenopause poses significant health risks for women, particularly an increased vulnerability to fractures associated with osteoporosis. Dietary interventions have emerged as promising strategies, focusing on mitigating the risk of osteoporos
Externí odkaz:
https://doaj.org/article/0169f1d41715468c937b67ba6abb0689
