اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSmoothness of radial solutions to Monge-Ampere equations
144
0
0.0
(
0
)
تأليف
Cristian Rios
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We characterize when radial weak solutions to Monge-Ampere equations are smooth. This paper extends previous partial results and also covers Generalized Monge-Ampere equations and infinitely vanishing right hand side.
قيم البحث
اقرأ أيضاً
We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampere-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equati
on of prescribed horizontal Gauss curvature in a Carnot group.
We prove a Harnack inequality for solutions to $L_A u = 0$ where the elliptic matrix $A$ is adapted to a convex function satisfying minimal geometric conditions. An application to Sobolev inequalities is included.
We find normal forms for parabolic Monge-Ampere equations. Of these, the most general one holds for any equation admitting a complete integral. Moreover, we explicitly give the determining equation for such integrals; restricted to the analytic case,
this equation is shown to have solutions. The other normal forms exhaust the different classes of parabolic Monge-Ampere equations with symmetry properties, namely, the existence of classical or nonholonomic intermediate integrals. Our approach is based on the equivalence between parabolic Monge-Ampere equations and particular distributions on a contact manifold, and involves a classification of vector fields lying in the contact structure. These are divided into three types and described in terms of the simplest ones (characteristic fields of first order PDEs).
In this note we obtain the characterization for asymptotic directions on various subgroups of the diffeomorphism group. We give a simple proof of non-existence of such directions for area-preserving diffeomorphisms of closed surfaces of non-zero curv
ature. Finally, we exhibit the common origin of the Monge-Ampere equations in 2D fluid dynamics and mass transport.
We prove the existence of entire solutions of the Monge-Amp`ere equations with prescribed asymptotic behavior at infinity of the plane, which was left by Caffarelli-Li in 2003. The special difficulty of the problem in dimension two is due to the glob
al logarithmic term in the asymptotic expansion of solutions at infinity. Furthermore, we give a PDE proof of the characterization of the space of solutions of the Monge-Amp`ere equation $det abla^2 u=1$ with $kge 2$ singular points, which was established by Galvez-Martinez-Mira in 2005. We also obtain the existence in higher dimensional cases with general right hand sides.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
