ﻻ يوجد ملخص باللغة العربية
We introduce a notion of quasilinear parabolic equations over metric measure spaces. Under sharp structural conditions, we prove that local weak solutions are locally bounded and satisfy the parabolic Harnack inequality. Applications include the parabolic maximum principle and pointwise estimates for weak solutions.
We bound the difference between solutions $u$ and $v$ of $u_t = aDelta u+Div_x f+h$ and $v_t = bDelta v+Div_x g+k$ with initial data $phi$ and $ psi$, respectively, by $Vert u(t,cdot)-v(t,cdot)Vert_{L^p(E)}le A_E(t)Vert phi-psiVert_{L^infty(R^n)}^{2r
We are concerned with nonexistence results for a class of quasilinear parabolic differential problems with a potential in $Omegatimes(0,+infty)$, where $Omega$ is a bounded domain. In particular, we investigate how the behavior of the potential near
We prove the continuity of bounded solutions for a wide class of parabolic equations with $(p,q)$-growth $$ u_{t}-{rm div}left(g(x,t,| abla u|),frac{ abla u}{| abla u|}right)=0, $$ under the generalized non-logarithmic Zhikovs condition $$ g(x,t,{rm
We describe the behavior of p-harmonic Greens functions near a singularity in metric measure spaces equipped with a doubling measure and supporting a Poincare inequality.
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 Holde