اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدEstimates of solutions for the parabolic $p$-Laplacian equation with measure via parabolic nonlinear potentials
171
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
For weak solutions to the evolutional $p$-Laplace equation with a time-dependent Radon measure on the right hand side we obtain pointwise estimates via a nonlinear parabolic potential.
قيم البحث
اقرأ أيضاً
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 Wolff potentials.
We study the parabolic $p$-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space-time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskii spaces and therefore c
over situations when the (gradient of) the solution has only fractional derivatives in space and time. The main novelty is that, different to all previous results, we do not assume any coupling condition between the space and time resolution $h$ and $tau$. The theoretical error analysis is complemented by numerical experiments.
Let $E subset mathbb R^{n+1}$ be a parabolic uniformly rectifiable set. We prove that every bounded solution $u$ to $$partial_tu- Delta u=0, quad text{in} quad mathbb R^{n+1}setminus E$$ satisfies a Carleson measure estimate condition. An important t
echnical novelty of our work is that we develop a corona domain approximation scheme for $E$ in terms of regular Lip(1/2,1) graph domains. This approximation scheme has an analogous elliptic version which is an improvement of the known results in that setting.
We obtain Dini and Schauder type estimates for concave fully nonlinear nonlocal parabolic equations of order $sigmain (0,2)$ with rough and non-symmetric kernels, and drift terms. We also study such linear equations with only measurable coefficients
in the time variable, and obtain Dini type estimates in the spacial variable. This is a continuation of the work [10, 11] by the first and last authors.
Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on $mathbb{R}^n$. In particular, in the case when $n=2$ they obtained Gaussian upper bound
estimates for the heat kernel without imposing further assumption on the coefficients. We study the fundamental solutions of the systems of second order parabolic equations in the divergence form with bounded, measurable, time-independent coefficients, and extend their results to the systems of parabolic equations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
