اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRegularity for critical points of convex functionals on Hessian spaces
135
0
0.0
(
0
)
تأليف
Arunima Bhattacharya
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider variational integrals of the form $int F(D^2u)$ where $F$ is convex and smooth on the Hessian space. We show that a critical point $uin W^{2,infty}$ of such a functional under compactly supported variations is smooth if the Hessian of $u$ has a small oscillation.
قيم البحث
اقرأ أيضاً
We give some generic properties of non degeneracy for critical points of functionals. We apply these results, obtaining some theorems of multiplicity of solutions for the equation -{epsilon}^2Delta_g u+u=|u|p-2u in M, u in H_g^1(M) where M is a compa
ct Riemannian manifold of dimension n and 2< p<2n/(n-2).
We consider Dirichlet problems for linear elliptic equations of second order in divergence form on a bounded or exterior smooth domain $Omega$ in $mathbb{R}^n$, $n ge 3$, with drifts $mathbf{b}$ in the critical weak $L^n$-space $L^{n,infty}(Omega ; m
athbb{R}^n )$. First, assuming that the drift $mathbf{b}$ has nonnegative weak divergence in $L^{n/2, infty }(Omega )$, we establish existence and uniqueness of weak solutions in $W^{1,p}(Omega )$ or $D^{1,p}(Omega )$ for any $p$ with $n = n/(n-1)< p < n$. By duality, a similar result also holds for the dual problem. Next, we prove $W^{1,n+varepsilon}$ or $W^{2, n/2+delta}$-regularity of weak solutions of the dual problem for some $varepsilon, delta >0$ when the domain $Omega$ is bounded. By duality, these results enable us to obtain a quite general uniqueness result as well as an existence result for weak solutions belonging to $bigcap_{p< n }W^{1,p}(Omega )$. Finally, we prove a uniqueness result for exterior problems, which implies in particular that (very weak) solutions are unique in both $L^{n/(n-2),infty}(Omega )$ and $L^{n,infty}(Omega )$.
We show that convex viscosity solutions of the Lagrangian mean curvature equation are regular if the Lagrangian phase has Holder continuous second derivatives.
We consider critical points of a class of functionals on compact four-dimensional manifolds arising from Regularized Determinants for conformally covariant operators, whose explicit form was derived in [10], extending Polyakovs formula. These corresp
ond to solutions of elliptic equations of Liouville type that are quasilinear, of mixed orders and of critical type. After studying existence, asymptotic behaviour and uniqueness of fundamental solutions, we prove a quantization property under blow-up, and then derive existence results via critical point theory.
In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument, using a recent global regularity of optimal transportation in convex domains by the authors.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
