اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the Greens matrices of strongly parabolic systems of second order
148
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We establish existence and various estimates of fundamental matrices and Greens matrices for divergence form, second order strongly parabolic systems in arbitrary cylindrical domains under the assumption that solutions of the systems satisfy an interior H{o}lder continuity estimate. We present a unified approach valid for both the scalar and the vectorial cases.
قيم البحث
اقرأ أيضاً
We study Greens matrices for divergence form, second order strongly elliptic systems with bounded measurable coefficients in two dimensional domains. We establish existence, uniqueness, and pointwise estimates of the Greens matrices.
We construct Greens functions for second order parabolic operators of the form $Pu=partial_t u-{rm div}({bf A} abla u+ boldsymbol{b}u)+ boldsymbol{c} cdot abla u+du$ in $(-infty, infty) times Omega$, where $Omega$ is an open connected set in $mathb
b{R}^n$. It is not necessary that $Omega$ to be bounded and $Omega = mathbb{R}^n$ is not excluded. We assume that the leading coefficients $bf A$ are bounded and measurable and the lower order coefficients $boldsymbol{b}$, $boldsymbol{c}$, and $d$ belong to critical mixed norm Lebesgue spaces and satisfy the conditions $d-{rm div} boldsymbol{b} ge 0$ and ${rm div}(boldsymbol{b}-boldsymbol{c}) ge 0$. We show that the Greens function has the Gaussian bound in the entire $(-infty, infty) times Omega$.
We establish existence and pointwise estimates of fundamental solutions and Greens matrices for divergence form, second order strongly elliptic systems in a domain $Omega subseteq mathbb{R}^n$, $n geq 3$, under the assumption that solutions of the sy
stem satisfy De Giorgi-Nash type local H{o}lder continuity estimates. In particular, our results apply to perturbations of diagonal systems, and thus especially to complex perturbations of a single real equation.
We construct fundamental solutions of second-order parabolic systems of divergence form with bounded and measurable leading coefficients and divergence free first-order coefficients in the class of $BMO^{-1}_x$, under the assumption that weak solutio
ns of the system satisfy a certain local boundedness estimate. We also establish Gaussian upper bound for such fundamental solutions under the same conditions.
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
