اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOptimal Holder regularity for nonautonomous Kolmogorov equations
82
0
0.0
(
0
)
تأليف
L. Lorenzi
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider a class of nonautonomous elliptic operators ${mathscr A}$ with unbounded coefficients defined in $[0,T]timesR^N$ and we prove optimal Schauder estimates for the solution to the parabolic Cauchy problem $D_tu={mathscr A}u+f$, $u(0,cdot)=g$.
قيم البحث
اقرأ أيضاً
Using time dependent Lyapunov functions, we prove pointwise upper bounds for the heat kernels of some nonautonomous Kolmogorov operators with possibly unbounded drift and diffusion coefficients.
We study a class of elliptic operators $A$ with unbounded coefficients defined in $ItimesCR^d$ for some unbounded interval $IsubsetCR$. We prove that, for any $sin I$, the Cauchy problem $u(s,cdot)=fin C_b(CR^d)$ for the parabolic equation $D_tu=Au$
admits a unique bounded classical solution $u$. This allows to associate an evolution family ${G(t,s)}$ with $A$, in a natural way. We study the main properties of this evolution family and prove gradient estimates for the function $G(t,s)f$. Under suitable assumptions, we show that there exists an evolution system of measures for ${G(t,s)}$ and we study the first properties of the extension of $G(t,s)$ to the $L^p$-spaces with respect to such measures.
This paper proves Holder continuity of viscosity solutions to certain nonlocal parabolic equations that involve a generalized fractional time derivative of Marchaud or Caputo type. As a necessary and preliminary result, this paper first shows that vi
scosity solutions to certain nonlinear ordinary differential equations involving the generalized fractional time derivative are Holder continuous.
We consider a class of nonautonomous second order parabolic equations with unbounded coefficients defined in $ItimesR^d$, where $I$ is a right-halfline. We prove logarithmic Sobolev and Poincare inequalities with respect to an associated evolution sy
stem of measures ${mu_t: t in I}$, and we deduce hypercontractivity and asymptotic behaviour results for the evolution operator $G(t,s)$.
We classify regularity for a class of Lagrangian mean curvature type equations, which includes the potential equation for prescribed Lagrangian mean curvature and those for Lagrangian mean curvature flow self-shrinkers and expanders, translating soli
tons, and rotating solitons. We first show that convex viscosity solutions are regular provided the Lagrangian angle or phase is $C^2$ and convex in the gradient variable. We next show that for merely Holder continuous phases, convex solutions are regular if they are $C^{1,beta}$ for sufficiently large $beta$. Singular solutions are given to show that each condition is optimal and that the Holder exponent is sharp. Along the way, we generalize the constant rank theorem of Bian and Guan to include arbitrary dependence on the Legendre transform.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
